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Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection
Shashank Kotyan, Makoto Shing, Yuki Imajuku, Rujikorn Charakorn, Tarin Clanuwat
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 95%
Last extracted: 8/20/2026, 4:39:31 AM
Summary
This paper introduces a diagnostic framework for AI-generated image (AIGI) detection using a 'Gaussian discriminant ladder' consisting of closed-form classifiers (Euc-NCM, Cos-NCM, GNB, Mah-NCM, QDA) fitted on frozen encoder features. Evaluated on the Percept-Lens suite (39 datasets, 7.1M images), the study demonstrates that these simple, prior-conditioned statistical baselines are often competitive with or exceed complex trained detector heads, highlighting the importance of the training prior and feature geometry in generalization under distribution shifts.
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Shashank Kotyan → affiliatedwith → Sakana AI
confidence 99% · Shashank Kotyan... Sakana AI, Tokyo, Japan
Percept-Lens → usedforevaluation → Gaussian Discriminant Ladder
confidence 98% · On Percept-Lens... the best rung is frequently competitive with... released AI-generated image detector heads
Gaussian Discriminant Ladder → includes → GNB
confidence 95% · We consider... Gaussian Naive Bayes (GNB)... as Gaussian discriminants.
Gaussian Discriminant Ladder → includes → Mah-NCM
confidence 95% · We consider... Mahalanobis Nearest Centroid Matching (Mah-NCM)... as Gaussian discriminants.
Gaussian Discriminant Ladder → includes → QDA
confidence 95% · We consider... Quadratic Discriminant Analysis (QDA)... as Gaussian discriminants.
Gaussian Discriminant Ladder → includes → Euc-NCM
confidence 95% · We include squared Euclidean nearest-centroid matching (Euc-NCM)... as Gaussian discriminants.
Gaussian Discriminant Ladder → includes → Cos-NCM
confidence 95% · we consider Cosine Nearest Centroid Matching (Cos-NCM)... as Gaussian discriminants.
Gaussian Discriminant Ladder → outperformsorcompeteswith → trained detector heads
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Abstract
Abstract:Diffusion-based generators have made synthetic images ubiquitous, but detectors often fail under simultaneous shifts in generator, prompt/style, and source-domain. We study AI-generated image detection as a transfer system described by training prior, frozen encoder feature space, and decision rule, and ask when classifier head training adds value beyond what is already separable in modern features. As a controlled diagnostic, we fit a prior-conditioned Gaussian discriminant ladder: closed-form heads built from first- and second-order feature statistics under nested covariance assumptions. On Percept-Lens, a unified protocol over 39 public datasets (7.1 million images), the best rung is frequently competitive with, and sometimes exceeds, released AI-generated image detector heads when matched on both prior and encoder. We further quantify strong sensitivity to the training prior, data-efficiency of moment-based heads, and representation dependence of Gaussian shift metrics, motivating (prior, encoder, head)-level reporting and stronger analytical baselines for AIGI transfer.
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- Source: https://arxiv.org/abs/2608.18523v1
- Canonical: https://arxiv.org/abs/2608.18523v1
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20 August 2026 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection Shashank Kotyan, Makoto Shing, Yuki Imajuku, Rujikorn Charakorn and Tarin Clanuwat Sakana AI, Tokyo, Japan Diffusion-based generators have made synthetic images ubiquitous, but detectors often fail under simultaneous shifts in generator, prompt/style, and source-domain. We study AI-generated image detection as a transfer system described by training prior, frozen encoder feature space, and decision rule, and ask when classifier head training adds value beyond what is already separable in modern features. As a controlled diagnostic, we fit a prior-conditioned Gaussian discriminant ladder: closed-form heads built from first- and second-order feature statistics under nested covariance assumptions. On Percept-Lens, a unified protocol over 39 public datasets (7.1 million images), the best rung is frequently competitive with, and sometimes exceeds, released AI-generated image detector heads when matched on both prior and encoder. We further quantify strong sensitivity to the training prior, data-efficiency of moment-based heads, and representation dependence of Gaussian shift metrics, motivating (prior, encoder, head)-level reporting and stronger analytical baselines for AIGI transfer. Keywords: AI-generated image detection; distribution shift; Gaussian discriminant analysis; few-shot transfer; transfer learning. Contents 1 Introduction2 2 Related Works3 3 Preliminaries4 4 Prior-Conditioned Gaussian Discriminants as Few-Shot Discriminant Heads4 5 Investigating Generalization with Percept-Lens suite7 6 Conclusion13 A On the Computational Paradigm and Practical Utility of Gaussian Discriminants21 B Proofs of Theoretical Propositions21 C Analytical Forms of the Gaussian Discriminant Ladder25 D Details about existing datasets in our Percept-Lens evaluation suite26 E Extended Investigation of Generalization with Percept-Lens suite27 F Threshold-Free (AUC) Evaluation on Mixed Datasets in Percept-Lens suite31 G Class-Conditional Gaussianity Diagnostics of Evaluation Features39 Corresponding author(s): Shashank Kotyan (shashank@sakana.ai) arXiv:2608.18523v1 [cs.CV] 19 Aug 2026 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection Image Encoder Support Set Real Images Support Set Fake Images Testing Images Image Encoder Feature Projections using pre-trained image encoders Support Set Real Images Features Support Set Fake Images Features Test Features Estimate Gaussian Parameters Estimate Gaussian Parameters 2D Visualization of Gaussian Ellipsoids and feature projections Image Encoder Figure 1|Training-prior-conditioned Gaussian discriminants in a frozen feature space. A frozen image encoder휙 maps images푥to embeddings푧. Given a (possibly few-shot) support setSdrawn from a training prior, we estimate class- conditional moments(휇 푐 ,Σ 푐 )and instantiate a ladder of classical closed-form heads under nested covariance assumptions. By keeping the encoder and prior fixed, the ladder isolates what the decision rule contributes. 1. Introduction Diffusion-based generative models (MidJourney, 2022; Ramesh et al., 2021; Rombach et al., 2022; Saharia et al., 2022) have made high-quality AI-generated imagery widely accessible. These models have practical benefits, but they also complicate trust in visual media and enable misuse of synthetic content (Bushard, 2023; Daniel, 2024; McCarthy, 2023). As a result, AI-generated image (AIGI) detection has become a core recognition problem with direct implications for safety and privacy. Modern detectors must transfer across shifts in both generator family and image-source domain. In practice these shifts co-occur (new generators, new prompting styles, new platforms, and post- processing), and performance can collapse even when in-distribution metrics look strong. Moreover, collecting large-scale labeled data from newly emerging generators is often expensive or infeasible. Together, these conditions make AIGI detection a concrete transfer / low-shot recognition problem, where a deployed detector must operate under joint shift and sometimes with only a small support set for calibration. Existing evaluations (Baraldi et al., 2025; Chen et al., 2024; Zhu et al., 2023) typically probe only part of this space, frequently reusing narrow prompt regimes and closely related sources. Such evaluations can conflate genuine generalization with prior-specific shortcuts. We take a stricter, system-level view. A reported number is a property of a system consisting of a training prior, a frozen image encoder, and a decision rule on top. Here, training prior denotes the data distribution induced by a public training dataset, such asCommunityForensics(Park and Owens, 2025); it is not a Bayesian prior over model parameters. If generalization fails, it is not obvious whether the bottleneck is the representation, the head optimization, or the prior itself. To isolate the decision-rule factor while keeping the prior and representation fixed, we fit training- prior-conditioned Gaussian discriminants, which are classical closed-form heads obtained from first- and second-order statistics of frozen encoder features (Figure 1). We organize these rules into a Gaussian discriminant ladder spanning nested covariance assumptions (isotropic, diagonal, shared, class- specific). Because each rung has an analytic solution, the ladder is a reproducible, hyperparameter- light baseline. The identity of the best-performing rung also indicates which low-order feature statistics transfer across generator and domain shifts. Although Gaussian discriminants are classical, 2 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection we argue that they are underused as diagnostic baselines in AIGI detection, and we find that they can be competitive under matched (prior, encoder) conditions. Empirically, across 39 public test sets (7.1 million images), at least one rung is often competitive with trained heads under matched priors and frozen encoders. As a retrospective diagnostic upper bound, the best rung can even surpass released heads in several settings. Our decomposition is not fully symmetric across the three factors. The most direct intervention is a matched head replacement, while the encoder and prior experiments are controlled one-factor sweeps. We use the procedure as a source-side audit. If a trained head does not outperform the best rule in the ladder on the same final representation and support prior, classifier training is unlikely to be the source of OOD transfer gains. If it succeeds, it signals structure beyond second moments. Contributions. Prior-conditioned Gaussian discriminant ladder (diagnostic baseline). We instantiate a ladder of classical closed-form Gaussian heads on frozen encoder features, varying covariance assumptions (isotropic→diagonal→shared full→class-specific full). The best-transfer rung provides an interpretable diagnostic of which low-order feature statistics are preserved under shift. Post-hoc controlled evaluation under matched (prior, encoder) conditions. On Percept-Lens, a unified evaluation protocol built entirely from existing public datasets, we compare released AI- generated image detector heads against the ladder using the same training prior and the same frozen encoder features. This isolates when trained heads add value beyond low-order geometry. Empirical drivers of generalization under joint shift. We quantify sensitivity to the training prior under a fixed encoder, show that moment-based heads can adapt with few labeled samples on strong frozen encoders, and demonstrate that Gaussian shift metrics are strongly representation- conditioned. 2. Related Works 2.1. AI-generated Image (AIGI) detection under Distribution Shift The literature on AIGI detection spans artifact-driven detectors (He et al., 2021; Wang et al., 2020; Yang et al., 2019) and representation-based detectors (Baraldi et al., 2025; Ojha et al., 2023; Park and Owens, 2025). Early work focused on GAN-era artifacts and domain-specific settings such as face forgeries (He et al., 2021; Wang et al., 2020; Yang et al., 2019). Diffusion models increased photorealism and prompt diversity, and exposed a persistent failure mode: detectors trained on narrow synthetic prior exploit shortcuts that do not transfer across generators or domains (Baraldi et al., 2025; Chen et al., 2024; Xiao et al., 2025; Zhu et al., 2023). Chen et al. (2024) and Park and Owens (2025) broaden training priors by scaling generator coverage. Ojha et al. (2023), Baraldi et al. (2025), and Zhou et al. (2025a) instead use foundation-model features and lightweight heads. Yang et al. (2026) adjust detector logits or thresholds after training under shift. Our intervention instead replaces the classifier in feature space while matching the prior and encoder. Thus our emphasis is not another trained detector, but what is already separable in frozen encoder space and what the trained head adds under the same prior. This is closely related to the observation that many OOD detectors can be expressed as generative scoring rules on features, but the implications for AIGI detection under joint shift have not been carefully isolated. 2.2. Analytical Gaussian Discriminants and Feature-Space Scoring Gaussian discriminant analysis and Mahalanobis scoring are classical tools for uncertainty and OOD detection (Lee et al., 2018). Wu et al. (2025b) connect few-shot prototypical inference to Euclidean 3 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection nearest-centroid rules, while Yan et al. (2025) explore orthogonal subspace decompositions that preserve pretrained structure under adaptation. We build on these ideas, but use them as a diagnostic ladder: isotropic, diagonal, tied, and class- specific covariance assumptions correspond to increasing geometric expressivity. The decision rules themselves are not new. Our contribution is to condition them on explicit training priors and use the ladder covariance model to interpret what transfers, and what does not, across generator and domain shifts. 3. Preliminaries 3.1. Problem setup We study binary detection of AI-generated images. Given a training setD train =(푥 푖 , 푦 푖 ) 푛 푖=1 , where 푥 푖 are images and푦 푖 ∈ 0,1are labels for real (푦=0) and synthetic (푦=1) images, the goal of AIGI detection is to learn a classifier that can accurately predict the label of a previously unseen image. 3.2. Feature Extraction and Trained Classifiers We use a frozen image encoder휙:X → ℝ 퐷 from a pre-trained foundation model to map each image 푥to a퐷-dimensional feature vector푧= 휙(푥). A standard approach trains a discriminative head, such as a linear probe, on these features by minimizing a loss function (e.g., binary cross-entropy) via gradient descent:min 푤,푏 Í 푛 푖=1 CE(휎(푤 ⊤ 푧 푖 + 푏), 푦 푖 )where휎(·)is the sigmoid activation function and 푤∈ ℝ 퐷 and 푏∈ ℝ define a separating hyperplane. More complex models, such as multi-layer perceptrons (MLPs), can learn non-linear decision boundaries. This process iteratively searches for an optimal boundary based on the training data. Although powerful, these methods can overfit to artifacts specific to the generative models in the training set, potentially limiting generalization to unseen generative processes (Park and Owens, 2025; Yan et al., 2025). We compare (i) trained discriminative detectors that optimize a supervised objective on a given prior and (i) Gaussian discriminant rule classifiers fitted on frozen features (Section 4). The audit applies to released systems that expose the feature vector used by a classifier, including frequency/statistical detectors (Frank et al., 2020; Yan et al., 2024), reconstruction-based detectors (Cazenavette et al., 2024; Chen et al., 2024), LoRA-adapted detectors (Yan et al., 2025), or end-to-end detectors (Baraldi et al., 2025; Wang et al., 2020) after their final representation is fixed. Methods that expose only a scalar anomaly score can still be evaluated by Percept-Lens as complete detectors, but their internal head cannot be replaced by the ladder. The split is diagnostic: if a trained head underperforms a closed-form rule under OOD shift, the trained head’s decision surface and/or training prior is implicated rather than only the encoder capacity. 4.Prior-Conditioned Gaussian Discriminants as Few-Shot Discriminant Heads We use Gaussian class-conditional models as a controlled diagnostic of what information is already separable in a frozen feature space. Motivated by classical generative classification and recent analyses of contrastive representations using mixture models (Bansal et al., 2025), we approximate 푝(푧 | 푦= 푐) ≈ N(휇 푐 ,Σ 푐 ), 푐 ∈ 0, 1.(4.1) Given a support setSdrawn from a training prior,S ⊆ D train , we estimate(휇 푐 ,Σ 푐 )by sample moments. We also define the pooled covarianceΣ 푝 = (푛 0 −1)Σ 0 +(푛 1 −1)Σ 1 푛 0 +푛 1 −2 , used when assuming a shared 4 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection Spherical (Isotropic) Covariance (Euclidean/Cosine Nearest Centroid Matching) Spread is the same in every dimension (no preferred direction), so similarity is basically Euclidean distance (magnitude) or Cosine distance (angular/direction) to the mean, and the decision boundary tends to look like a nearest-centroid split. Diagonal Covariance (Gaussian Naive Bayes) Spread can differ per dimension but dimensions don’t co- vary (no rotation), so distance is like Euclidean after per- dimension re-scaling, and the boundary can bend but stays constrained by axis-aligned geometry. Homoscedastic Covariance (Mahalanobis Nearest Centroid Matching) All classes share the same covariance (same ellipse shape for everyone), so differences come mainly from where the means are, and the decision boundary becomes linear. Heteroscedastic Covariance (Quadratic Discriminant Analysis) Each class has its own covariance including correlations (rotated ellipses allowed), so the model adapts to class- specific geometry, and the decision boundary becomes quadratic/curvy. Equal Spread Non-Equal Spread Non-aligned but constrained spreads (along axes) Equal Spread Aligned non-constrained spreads Non-Equal Spread Non-aligned, non-constrained spread Figure 2|Gaussian discriminant ladder as nested covariance assumptions. Each rung is a classical generative classifier obtained by restricting the class-conditional covariance: isotropic (Euc-/Cos-NCM), diagonal (GNB), shared full covariance (Mah-NCM), or class-specific full covariance (QDA). This nested family makes it possible to diagnose how much transferable signal is captured by first- and second-order feature statistics. covariance structure. In high-dimensional embeddings, covariance inversion can be ill-conditioned. We therefore use standard regularization (diagonal loading and shrinkage) when computingΣ −1 and log-determinants (Appendix Section D). The Gaussian assumption is diagnostic rather than literal. Appendix Tables 23 and 24 shows mostly near-Gaussian marginal summaries on PE-Core features, but also clear failures such asFourierSpectrumDiscrepancies(Dzanic et al., 2020) andDiffusionForensics-fake (Wang et al., 2023). Multimodal or heavy-tailed regimes are exactly where trained non-linear heads may add value. This yields a ladder of classical discriminant rules in closed form, and the best-performing covariance assumption becomes an interpretable indicator of which feature statistics transfer across domains, bypassing iterative training. (The same estimation extends to푁-way퐾-shot classification. We focus on binary AIGI detection.) In this article, we consider Cosine Nearest Centroid Matching (Cos-NCM), Gaussian Naive Bayes (GNB), Mahalanobis Nearest Centroid Matching (Mah-NCM), and Quadratic Discriminant Analysis (QDA) as Gaussian discriminants. We also include squared Euclidean nearest-centroid matching (Euc-NCM), which mirrors the inference rule used in prototypical-network detectors (e.g. Wu et al., 2025b) but is applied directly in the frozen encoder space without metric learning. Table 1 provides an overview of Gaussian discriminants in analytical form, while Figure 2 provides a visual explanation. Euclidean Nearest Centroid Matching (Euc-NCM). Assuming an isotropic shared covariance Σ 푐 = 휎 2 퐼, the Gaussian log-likelihood (up to additive constants) is proportional to the squared Euclidean distance to the class mean. Prediction reduces to nearest-centroid classification in the frozen feature space, matching prototypical inference without metric learning. Cosine Nearest Centroid Matching (Cos-NCM). When features areℓ 2 -normalized, isotropic Gaussian scoring is monotone in cosine similarity. Cos-NCM predicts the class whose centroid has the highest cosine similarity to the query. Gaussian Naive Bayes (GNB). GNB assumes diagonal covarianceΣ 푐 = diag(휎 2 푐,1 , . . . , 휎 2 푐,퐷 ), which implies conditionally independent features. The assumption simplifies classification but ignores feature correlations. 5 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection Table 1|Gaussian discriminant ladder used as analytical baselines. Each rung is a generative classifier obtained by restricting the class-conditional covariance (isotropic, diagonal, homoscedastic, or heteroscedastic), which determines the geometry of the induced decision boundary. We use this ladder to isolate head effects in a fixed frozen encoder feature space rather than to propose a new detector. Gaussian DiscriminantCovariance Structure Assumption Decision Boundary Characteristic Euclidean Nearest Centroid Matching (Euc-NCM) IsotropicΣ 푐∈0,1 = 휎 2 퐼LinearAssumes spherical class distributions. Cosine Nearest Centroid Matching (Cos-NCM) IsotropicΣ 푐∈0,1 = 휎 2 퐼LinearAssumes spherical class distributions; decision is based on angular proximity, suitable for normalized embeddings. Gaussian Naive Bayes (GNB) DiagonalΣ 푐∈0,1 = diag(휎 2 푐,푗 ) Non-Linear Simplest model; assumes feature independence, useful for identifying decorrelated representations. MahalanobisNearest Centroid Matching (Mah- NCM) HomoscedasticΣ 0 =Σ 1 =Σ 푝 LinearAssumes classes share the same elliptical shape. It accounts for feature correlations by whitening the space, yielding a correlation-aware linear boundary. QuadraticDiscriminant Analysis (QDA) HeteroscedasticΣ 0 ≠Σ 1 Quadratic Most general model; allows each class to have a unique elliptical shape and orientation, capturing complex separations. Mahalanobis Nearest Centroid Matching (Mah-NCM). Mah-NCM assumes homoscedasticity, i.e., a shared covariance matrix for both classesΣ 0 =Σ 1 =Σ 푝 . The classification decision is based on the Mahalanobis distance(푧− 휇 푐 ) ⊤ Σ −1 푝 (푧− 휇 푐 ), which accounts for the correlations of the features by transforming the feature space into one in which the pooled covariance is the identity. Quadratic Discriminant Analysis (QDA). QDA is the most general of the four classifiers, allowing each class to have its own full-rank covariance matrix (Σ 0 ≠Σ 1 ), thus assuming heteroskedasticity. The resulting quadratic boundary can adapt to classes with different shapes and orientations. 4.1. Connection to classical generative classification The efficacy of these Gaussian discriminants in analytical form can be understood through the lens of Bayesian decision theory, which provides a formal basis for our geometric approach. Under the Gaussian assumption, they approximate or realize the Bayes-optimal classifier, which minimizes the probability of error. Full proofs are provided in the Appendix Section B. Proposition 1 (Bayes-Optimal Classifier under Gaussian Assumption). If the class-conditional densities are Gaussian,푝(푧 | 푦= 푐) ≈ N(휇 푐 ,Σ 푐 ), and the class priors are equal,푃(푦=0)= 푃(푦=1)= 1 2 , the Bayes-optimal decision rule is given by Quadratic Discriminant Analysis (QDA). Proposition 2 (Optimality under Homoscedasticity). If the classes are additionally assumed to be homoscedastic (i.e., they share a common covariance matrixΣ 0 =Σ 1 =Σ 푝 ), the Bayes-optimal decision rule simplifies to Mahalanobis Nearest Centroid Matching (Mah-NCM). Proposition 3 (Performance Stability under Bounded Drift). Assume a homoscedastic classifier with shared covarianceΣand equal priors. If the statistical drift between the training and testing distributions is bounded by∥휇 test 푐 − 휇 train 푐 ∥ 2 ≤ 휖 휇 and∥Σ test −Σ train ∥ 퐹 ≤ 휖 Σ , then|AUC test −AUC train | ≤ 퐿(휖 휇 +휖 Σ )where 퐿 is the Lipschitz constant. Proposition 4 (Stability of the Fisher Margin under Distributional Drift). Assume that both the training and testing domains are characterized by homoscedastic Gaussian parameters. If the distributional drift is bounded such that∥훿 test −훿 train ∥ 2 ≤ 휖and∥Σ test 푝 −Σ train 푝 ∥ 퐹 ≤ 휂, where훿= 휇 1 −휇 0 , then the absolute change 6 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection in the Fisher MarginD 휇 is bounded, to a first order, by|D test 휇 −D train 휇 | ≤2∥(Σ train 푝 ) −1 ∥ 2 ∥훿 train ∥ 2 휖+ 푂(휂). These propositions should be read as model-conditional: they characterize the optimal decision rules if frozen features are well-approximated by Gaussian class-conditionals. They provide the theoretical foundation for our geometric analysis of generalization. Under this model, Quadratic Discriminant Analysis is Bayes-optimal in the heteroscedastic case (Proposition 1) and simplifies to a linear rule under a shared covariance (Mahalanobis-NCM; Proposition 2). Proposition 3 shows that, under the homoscedastic Gaussian model, the AUC of Mah-NCM is a monotone function of the Fisher marginD 휇 . Proposition 4 bounds howD 휇 changes under drift in low-order statistics. Together, these results imply smooth degradation when class means and covariances drift. In this model, reliable generalization requires geometric alignment between training and testing data. The linear decision boundary of Mah-NCM has the same functional form as a linear probe trained with cross-entropy. Both induce a single separating hyperplane in푧-space. The key difference is optimization rather than representation. A neural network iteratively searches for the boundary, whereas Gaussian discriminants compute it analytically from the data’s first- and second-order statistics. Thus, when a trained linear head does not outperform Gaussian discriminants under matched priors and encoders, the result is consistent with the hypothesis that second-order feature geometry is already sufficient for separation. Consistent gaps instead suggest non-Gaussian or higher-order structure that the ladder cannot capture. Limitations. By design, the Gaussian ladder is restricted to a Gaussian class-conditional approximation based on first- and second-order statistics. The result is a diagnostic baseline rather than a universal detector, one that leaves out higher-order, multimodal, or heavy-tailed cues from strong post-processing, unusual content, or generator-specific artifacts. In those regimes, trained non-linear heads or end-to-end adaptation can legitimately outperform the ladder. 5. Investigating Generalization with Percept-Lens suite We use the Gaussian ladder to investigate which components of a detection system drive OOD performance under realistic distribution shift. We focus on the training prior, the frozen encoder, and the decision rule on top. To assess the reliability of current AI-generated image detectors under realistic generative variability, we begin by evaluating pre-trained models on the Percept-Lens test suite. These results help to localize whether failures are attributable to the training prior, the encoder feature space, or the trained decision surface, motivating more principled system-level investigations. 5.1. Evaluation Protocol and Data Percept-Lens denotes a unified evaluation protocol constructed entirely from existing public datasets to stress-test AIGI detectors under joint distribution shift. Unlike settings where only the generator family changes while the underlying image source and prompt distribution remain fixed, Percept-Lens explicitly couples shifts in generator family, prompt/style, and acquisition pipeline (Figure 3). To avoid conflating in-distribution performance with transfer, the large training priors used for conditioning (e.g., CommunityForensics, GenImage, DRCT-2M, ELSA-D3) are treated as support-only and are not part of the evaluation suite. Evaluation Datasets. The Percept-Lens suite aggregates 39 existing public datasets totaling 7.1 million images. It spans real-only, synthetic-only, and mixed regimes, with joint shifts in (i) generator family, (i) prompt/style, and (i) image-source domain and post-processing. Concretely, it combines in-the-wild real sources, synthetic-only prompt/style collections, and mixed forensic benchmarks spanning diverse generators and post-processing. 7 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection Training Distribution Existing Evaluation Suite Type (1): Different Generative Models Existing Evaluation Suite Type (2): Different Data Sources Percept-Lens Evaluation Suite: Different Generative Models and Data Sources Uses some data source (e.g. one of ImageNet-1k, COCO, LAION-400M) and generative model to train the AI-Generated Image Detectors Uses some different generative model (e.g. Stable Diffusion XL-Turbo, Stable Diffusion v1.4) to evaluate the trained AI-Generated Image Detectors Uses some different data source (e.g. DiffusionDB, AI-Artworks) to evaluate the trained AI-Generated Image Detectors Uses different data sources (Art, Social-Media, Face, User-generated) and generative models (e.g. Stable Diffusion, FLUX, MidJourney, and various GANs) to evaluate the AI-Generated Image Detectors Figure 3|Percept-Lens stress-tests detectors under joint distribution shift. Percept-Lens is an evaluation protocol built entirely from existing public datasets. Many AIGI evaluations vary either the generator family or the image source in isolation; we instead evaluate under joint shifts in generator family, prompt/style, and source domain, closer to deployment where these factors drift together. Table 2|Closed-form Gaussian discriminants versus released AI-generated image detector heads under matched (prior, encoder) conditions. Mean class accuracyCA(dataset-wise balanced accuracy where defined; Section 5.1), macro- averaged across Percept-Lens evaluation datasets. For each released detector checkpoint, we report (i) the released decision head (Out-of-the-Shelf) and (i) closed-form baselines fitted on the same frozen encoder features using the corresponding public training prior: Euc-NCM (Wu et al., 2025b) and the best-performing rung of the Gaussian ladder. The full ladder is reported in Table 3. (Parentheses indicate the training subset reported by the original work when applicable.) Detection ModelOut-of-the-Shelf Euc-NCM (Wu et al., 2025b)Gaussian ladder (best) Trained with CNNSpot (Wang et al., 2020) (ProGAN Images based on LSUN) UnivFD (Ojha et al., 2023)54.63%50.98%57.62% (Mah-NCM) (2.99%↑) AIDE (Yan et al., 2024)56.41%54.25%62.76% (Mah-NCM) (6.35%↑) Trained with GenImage (Zhu et al., 2023) (Diffusion Model Images based on ImageNet-1k) AIDE (GenImage-SDv1) (Yan et al., 2024)48.99%54.53%57.35% (Mah-NCM) (8.36%↑) Effort (GenImage-SDv1) (Yan et al., 2025)72.58%75.06%76.82% (Mah-NCM) (4.24%↑) DRCT-UnivFD (Full GenImage) (Chen et al., 2024)65.77%66.08%73.01% (Mah-NCM) (7.24%↑) AIDE (Full GenImage) (Yan et al., 2024)54.98%52.24%64.64% (Mah-NCM) (9.66%↑) Trained with DRCT-2M (Chen et al., 2024) (Stable Diffusion Model Images based on COCO) DRCT-UnivFD (DRCT-SDv1) (Chen et al., 2024)63.36%65.36%70.20% (QDA) (6.84%↑) DRCT-UnivFD (DRCT-SDv2) (Chen et al., 2024)62.37%66.31%70.31% (QDA) (7.94%↑) Trained with ELSA-D3 (Baraldi et al., 2025) or CommunityForensics (Park and Owens, 2025) (Diffusion Model Images based on LAION-400M Dataset) CoDE-kNN (ELSA-D3) (Baraldi et al., 2025)64.01%63.63%66.15% (Mah-NCM) (2.14%↑) CF-224 (CommunityForensics) (Park and Owens, 2025)81.98%78.53%82.61% (Mah-NCM) (0.63%↑) CF-384 (CommunityForensics) (Park and Owens, 2025)87.54%82.65%84.55% (Mah-NCM) (–2.99%↓) Frozen image encoder (no detection fine-tuning) PE-Core-bigG-14-448 (Bolya et al., 2025)—86.38%94.46% (Mah-NCM) Percept-Lens standardizes evaluation over existing public datasets to ensure head–prior–encoder comparisons are tested under a realistic mixture of shifts. The complete manifest of the dataset and the composition of the class are provided in Appendix Table 9. Evaluation Protocol. For a training prior, detectors are evaluated on every dataset in the Percept- Lens test suite. We report a dataset-wise class accuracy that equals balanced accuracy when both classes are present and reduces to class-conditional accuracy on one-class sets. Concretely, for an evaluation dataset 푡 with observed classesC 푡 ⊆ 0, 1, we define Class Accuracy CA as 8 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection Table 3|Comparative Performance of Different Gaussian Discriminants. Mean class accuracyCA(macro-averaged across Percept-Lens evaluation datasets) for each rung of the Gaussian discriminant ladder, conditioned on the same public training prior and fitted on the same frozen features as in Table 2. (Parentheses indicate the training subset reported by the original work; underlining denotes improvement over the corresponding released head as reported in Table 2.) Detection ModelCos-NCMGNB Mah-NCMQDA Trained with CNNSpot (Wang et al., 2020) (ProGAN Images based on LSUN Dataset) UnivFD (Ojha et al., 2023)51.01% 48.44%57.62%48.23% AIDE (Yan et al., 2024)54.36% 56.69%62.76%61.28% Trained with GenImage (Zhu et al., 2023) (Diffusion Model Images based on ImageNet-1k Dataset) AIDE (GenImage-SDv1) (Yan et al., 2024)54.23%54.39%57.35%57.15% Effort (GenImage-SDv1) (Yan et al., 2025)74.44%74.92%76.82%73.21% DRCT-UnivFD (Full GenImage) (Chen et al., 2024)67.97%68.28%73.01%69.74% AIDE (Full GenImage) (Yan et al., 2024)52.66% 53.92%64.64%56.20% Trained with DRCT-2M (Chen et al., 2024) (Stable Diffusion Model Images based on COCO Dataset) DRCT-UnivFD (DRCT-SDv1) (Chen et al., 2024)65.16%66.37%65.21%70.20% DRCT-UnivFD (DRCT-SDv2) (Chen et al., 2024)65.53%66.69%67.91%70.31% Trained with ELSA-D3 (Baraldi et al., 2025) or CommunityForensics (Park and Owens, 2025) (Diffusion Model Images based on LAION-400M Dataset) CoDE-kNN (ELSA-D3) (Baraldi et al., 2025)62.70% 65.98% 66.15%64.00% CF-224 (CommunityForensics) (Park and Owens, 2025)78.98% 79.45%82.61%80.70% CF-384 (CommunityForensics) (Park and Owens, 2025)84.46% 80.01%84.55% 79.52% Frozen image encoder (no detection fine-tuning) PE-Core-bigG-14-448 (Bolya et al., 2025)86.06% 87.26%94.46% 86.15% CA (휙) (푡)= 1 |C 푡 | ∑︁ 푐∈C 푡 Pr(ˆ푦 휙 = 푐 | 푦= 푐),(5.1) and report the macro-average 1 |T| Í 푡∈T CA(푡)across evaluation datasetsTso that no single large dataset dominates. For all detectors we use the defaultarg maxdecision on predicted class probabilities and do not tune thresholds per dataset. On real-only sets,CAcorresponds to true-negative accuracy (1–FPR); on synthetic-only sets it corresponds to true-positive accuracy (1–FNR). We additionally compute AUC on the 24 mixed datasets (those containing both real and synthetic images) and report in Appendix Section F. 5.2. Closed-form Gaussian Discriminants versus Trained Heads Tables 2 and 3 compares released AI-generated image detector heads with Gaussian discriminant rules fitted on the same frozen features and conditioned on the same training prior. Several rows in Tables 2 and 3 share the same underlying backbone.UnivFDandDRCT-UnivFDboth use ViT-L-14-quickgelu-openai(Radford et al., 2021) as the image encoder; differences arise from the public training prior and the trained head.DRCTexposes classifier features after reconstruction training.Effortapplies LoRA adaptation before its head.AIDEuses frequency/statistical experts plus semantic features, andCoDE/CFtrain backbones and heads end-to-end. All are auditable once the encoder’s final feature space is exposed. Across several priors, the best closed-form Gaussian discriminant improves class accuracy, with the largest gains occurring when separation is well-captured by first- and second-order moments (often Mah-NCM). These patterns are consistent with Propositions 1 and 2: when separation is well-captured by first- and second-order moments in a frozen encoder feature space, the corresponding Gaussian 9 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection Table 4|Encoder scaling under a fixed prior: representation choice strongly affects transfer. Mean class accuracy CA(macro-averaged across Percept-Lens evaluation datasets) for Gaussian discriminant heads conditioned on the same CommunityForensicstraining prior (Park and Owens, 2025), using frozen CLIP encoders of increasing capacity pretrained by OpenAI. Only the head is changed. No detector fine-tuning is performed. Frozen EncodersEuc-NCM (Wu et al., 2025b) Cos-NCMGNB Mah-NCMQDA ResNet-50 (Timm, 2024a)65.27%64.36% 65.72%72.00% 63.15% ResNet-101 (He et al., 2016)65.20%64.70% 64.46%70.27% 62.29% ResNet-50x4 (Timm, 2024c)66.24%65.91% 65.12%72.34% 64.28% ResNet-50x16 (Timm, 2024b)67.35%66.77% 66.21%74.98% 65.71% ResNet-50x64 (Timm, 2024d)68.42%68.19% 65.02%74.57% 68.38% ViT-B/16 (Laion, 2024d)64.66%64.65% 66.37%74.18% 65.70% ViT-B/32 (Laion, 2024e)64.53%64.25% 64.83%70.61% 62.81% ViT-L/14 (Radford et al., 2021)66.18%68.44% 69.79%76.96% 68.87% Table 5|Pretraining objective affects transfer even without detector training. Mean class accuracyCA(macro-averaged across Percept-Lens evaluation datasets) for Gaussian discriminant heads conditioned on the sameCommunityForensics training prior (Park and Owens, 2025), using frozen encoders trained with different objectives. Frozen EncodersEuc-NCM (Wu et al., 2025b) Cos-NCMGNB Mah-NCMQDA MAE-Huge (He et al., 2022)55.18%55.22% 58.33%69.37% 64.01% BEiT-Large (Bao et al., 2022)58.53%58.49% 58.80%61.78% 53.63% CLIP-XLM-RoBERTa-Large (Cherti et al., 2023)70.72%69.70% 70.61%77.67% 65.79% SigLIP-Large (Zhai et al., 2023)58.25%58.25% 58.07%64.14% 60.85% BLIP-Large (Li et al., 2022)55.75%56.89% 53.87%70.17% 55.42% BLIP2 (Li et al., 2023)68.61%68.46% 65.41%77.73% 62.21% DINOv2-giant (Oquab et al., 2024)63.15%63.59% 61.95%73.30% 58.52% DINOv3-ViT-7b (Siméoni et al., 2025)83.85%85.82% 83.18%88.91% 78.88% discriminants recover most of the available discriminative geometry. A main exception isCF-384 (Park and Owens, 2025), where the released detector remains ahead of the ladder (87.54% vs. 84.55% CA), consistent with a regime in which the trained head’s decision surface exploits structure not explained by second-order moments alone. Per-dataset results in Tables 14 and 21 also show large variability. For example, Mah-NCM reaches near-ceiling performance on many synthetic-only sets but is much weaker onDeepFakeBench(Yan et al., 2023), while QDA performs best onCelebA-Spoof (Zhang et al., 2020). 5.3. Encoder Sensitivity of Closed-form Gaussian Discriminants We investigate the model-agnostic behavior of the ladder by evaluating a range of frozen architectures and pretraining objectives (Tables 4 and 5). Mah-NCM is consistently the top performer across these encoders, indicating that a shared full-covariance geometry captures a stable component of real/fake separability in modern representation spaces. This motivates a practical reporting guideline. Trained heads on frozen encoders should be compared against the best Gaussian rung on the same frozen features. Additional models are presented in Appendix Section E. 5.4. Training Prior Sensitivity of Closed-form Gaussian Discriminants We isolate training-prior effects by fixingPE-Core-bigG-14-448(Bolya et al., 2025) as the encoder and varying only the support prior used to estimate Gaussian parameters (Table 6). The spread is large: the best CA ranges from 77.92% (CNNSpot) to 94.46% (CommunityForensics), despite using the same representation and evaluation suite. Moreover, the prevailing covariance assumption shifts with the prior:DRCT-2Mfavors QDA 10 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection Table 6|Training prior dominates transfer even under a fixed encoder. Mean class accuracyCA(macro-averaged across Percept-Lens evaluation datasets) for Gaussian discriminant heads when varying only the support prior used to estimate moments, under the fixed frozenPE-Core-bigG-14-448encoder (Bolya et al., 2025). Underlining denotes improvement over the best released head of CF-384 (Park and Owens, 2025) as reported in Table 2. Training DatasetEuc-NCM (Wu et al., 2025b) Cos-NCMGNB Mah-NCMQDA CNNSpot (Wang et al., 2020)74.95%78.57% 59.21%77.93% 49.24% GenImage (Zhu et al., 2023)86.68%88.75%87.50%92.43%81.83% GenImage-SDv188.74%89.80%86.34%92.57%65.06% DRCT-2M (Chen et al., 2024)81.90%81.76% 86.21%83.25% 91.09% DRCT-SDv1 (Chen et al., 2024)82.29%83.81% 88.70%88.31%89.92% DRCT-SDv2 (Chen et al., 2024)83.50%84.38% 89.56%90.08%91.44% ELSA-D3 (Baraldi et al., 2025)88.87%89.03%86.98%94.45%86.40% CommunityForensics (Park and Owens, 2025)86.38%86.06% 87.26%94.46%86.15% Table 7|Data-efficiency of moment-based heads. Mean class accuracyCA(macro-averaged across Percept-Lens evaluation datasets) for Gaussian discriminant heads as the support set used to estimate moments is subsampled from CommunityForensics(Park and Owens, 2025), under the fixed frozenPE-Core-bigG-14-448encoder (Bolya et al., 2025). (Superscript/subscript denote max/min deviations (in percentage points) from the reported mean). Amount Euc-NCM (Wu et al., 2025b) Cos-NCMGNBMah-NCMQDA 0.001%83.97% +1.93 −2.74 83.46% +2.25 −2.47 87.14% +1.21 −1.68 85.56% +1.84 −1.75 85.13% +1.07 −0.66 0.005%86.04% +0.28 −0.40 85.78% +0.27 −0.53 87.23% +0.76 −0.77 90.89% +0.73 −1.34 85.53% +1.51 −1.71 0.01%86.32% +0.67 −0.35 86.02% +0.77 −0.42 87.42% +1.19 −0.90 91.55% +0.67 −0.69 86.48% +1.16 −0.82 0.1%86.26% +0.71 −0.44 85.92% +0.74 −0.47 87.33% +0.22 −0.19 93.18% +0.42 −0.54 84.18% +0.33 −0.71 1%86.39% +0.11 −0.12 86.05% +0.11 −0.10 87.28% +0.04 −0.05 93.52% +0.28 −0.17 85.16% +0.20 −0.34 100%86.38%86.06%87.26%94.46%86.15% (heteroscedastic) while all others favor Mah-NCM (homoscedastic). Thus, if two papers use the same backbone but different priors, their OOD behavior can differ more than what is attributable to the classifier family within the Gaussian ladder. 5.5. Data Efficiency of Closed-form Gaussian Discriminants We investigate data efficiency by subsampling the support set used to estimate Gaussian parameters (Table 7). Performance saturates quickly. With only 1% of the prior (around 43k samples), Mah-NCM nearly matches the full-support estimate, while at extremely small support sizes (0.001% of the prior, or 44 samples) the diagonal GNB assumption can be more stable. The pattern reinforces the central observation from the ladder. For this support prior and encoder, low-order feature statistics capture a large share of the signal used by the best head, without iterative optimization. With the frozenPE-Core-bigG-14-448encoder (Bolya et al., 2025), Mah-NCM fitted from only 0.005% of theCommunityForensicsprior (219 labeled samples) reaches 90.89% CA. Although this is not an apples-to-apples comparison toCF-384(which uses a different backbone), it indicates that moment-based adaptation can be data-efficient once the representation is strong. 5.6. Representation Sensitivity of Wasserstein-2 Shift Estimates All geometric shift metrics in Percept-Lens are computed in the encoder’s feature space, hence their numerical values are not purely properties of the data distributions, but of the encoder used to embed them. This raises a basic reliability question about whether conclusions drawn from a Gaussian shift metric are stable under reasonable encoder changes, or are artifacts of a particular backbone. 11 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection GenImageCommunityForensics ELSA_D3 DRCT-2MCNNSpotMean Training Priors FourierSpectrumDiscrepancies AnimeFace AGIQA-3k GANGen-Detection AGIQA-1k DeepFakeFace AnimeImages RobustLDM SynthScars LDMFakeDetect GigaGAN DNFTestSet Co-Spy-Bench AIGIBench LatentDiffusion AIGCDetect CNN_synth_testset AI-Artwork UFD B-Free FakeInversion Diffusion1kStep CelebA_Spoof DIF AIGI-Holmes Dalle3 SynthBuster InstagramImagesWithCaptions DiTFake DalleRecognition MidjourneyV6 AIGI-Detection-Quality-Paradox LASTED Chameleon Unsplash RealRobustBench DiffusionForensics SPAI DeepfakeBench Mean Test Sets 0.230.390.70.994.7 1.50.233.70.471.7 0.550.751.20.76.5 0.952.72.23.21.2 0.41.31.45.43.7 1.30.983.10.576.3 2.52.71.14.72.6 1.832.40.67.9 1.73.12.91.17.1 23.22.40.548.3 3.60.83.46.32.7 2.31.62.63.47.5 2.84.61.21.48 33.52.64.35.6 5.80.52.44.75.8 3.21.82.34.47.6 4.82.72.56.73.9 3.32.84.82.37.9 3.82.83.55.55.5 1.53.13.22.611 3.14.15.31.57.7 3.14.12.17.25.8 4.33.34.24.26.4 4.92.23.974.5 2.43.33.44.29.8 46.44.118.6 3.95.33.83.67.7 3.33.26.738.2 3.864.51.812 4.95.54.16.47 5.46.55.44.99.4 5.25.86.94.39.9 75.35.68.76 5.65.66.95.310 5.65.29.34.49.7 5.26.26.46.410 7.16.65.3 127.3 6.98.87.77.99.4 8.88.67.1115.8 1.41 1.53 1.93 2.04 2.43 2.45 2.72 3.14 3.18 3.28 3.37 3.46 3.61 3.81 3.84 3.88 4.13 4.23 4.25 4.32 4.36 4.45 4.47 4.51 4.62 4.85 4.87 4.87 5.55 5.57 6.31 6.43 6.52 6.78 6.84 6.89 7.66 8.12 8.21 3.633.713.914.216.96 4.48 Spearman Correlation of | Wasserstein2| and | Class Accuracy| Between CF-224 and CF-384 is -0.150 (p=0.0366) 0 5 10 15 20 25 30 | Wasserstein2| CNNSpotCommunityForensicsGenImage ELSA_D3 DRCT-2MMean Training Priors LatentDiffusion LASTED AIGCDetect SPAI MidjourneyV6 AIGIBench DIF Co-Spy-Bench AIGI-Holmes DeepfakeBench SynthScars UFD Dalle3 GigaGAN DiTFake Diffusion1kStep SynthBuster CNN_synth_testset DNFTestSet DiffusionForensics B-Free AGIQA-3k AIGI-Detection-Quality-Paradox GANGen-Detection Chameleon DalleRecognition RobustLDM LDMFakeDetect AGIQA-1k RealRobustBench FakeInversion AI-Artwork DeepFakeFace Unsplash CelebA_Spoof AnimeImages InstagramImagesWithCaptions FourierSpectrumDiscrepancies AnimeFace Mean Test Sets 3.91.91.33.85.8 5.23.24.93.14.2 3.85.73.16.47.3 9 1421.34 6.9100.454.38.3 5.14.26.26.98.4 6.75.48.26.75.9 7.13.34.99.39.4 4.87.5128.31.6 9.256.47.55.9 5.50.745.98.7 14 6.48.54.98.47.2 6.33.43.210 13 7.4107.86.77.9 69.111 132 8.98.78.29.17.5 4.41.39.41215 9.38.4118.76.3 6.78.68.67.4 12 8.27.3109.89.1 8.211 12133.4 3.689.911 16 11107.98.813 15 6.811911 11101010 15 1415 109.89 9.16.9 121318 9.17.6131318 1.6159.51917 1111141314 1011131619 7.914161419 9.112201721 1520171819 2118231922 2620222222 2323272126 2925262426 2825282828 3.35 4.11 5.27 6.04 6.06 6.15 6.57 6.78 6.78 6.8 6.91 7.1 7.17 7.97 8.23 8.49 8.56 8.7 8.7 8.91 9.57 9.72 10 10.5 11.4 11.5 11.7 12 12.6 12.6 14 14.2 15.8 18 20.6 22.1 24 26.1 27.5 10.110.211.111.512.6 11.1 Spearman Correlation of | Wasserstein2| and | Class Accuracy| Between PE-Core-bigG-14-448-meta and CF-384 is -0.194 (p=0.00657) 0 5 10 15 20 25 30 | Wasserstein2| Figure 4|Gaussian Wasserstein-2 distances are representation-conditioned. Each cell reports the absolute difference in class-averaged GaussianW 2 for the same train–test pair under two feature spaces,ΔW 2 (D train ,D test ;휙 푎 , 휙 푏 )(row/column means on the margins). The sub-figure title reports the Spearman correlation between the flattened cell-wiseΔW 2 values and the correspondingΔCAvalues. Large changes inW 2 do not necessarily coincide with large changes in Mah-NCM CA, so feature-space shift magnitudes should not be interpreted as detector-agnostic indicators without checking stability across representations. Setup. For each training priorD train and test setD test , class-conditional Gaussians are fitted to the representation induced by an encoder휙, then a class-averaged Wasserstein-2 shift is computed between the training and test distributions: W (휙) 2 (D train ,D test )= 1 2 ∑︁ 푐∈0,1 W 2 N(휇 (휙) 푐,D train ,Σ (휙) 푐,D train ),N(휇 (휙) 푐,D test ,Σ (휙) 푐,D test ) .(5.2) To isolate representation effects while keeping the data fixed, Figure 4 uses heatmap cells for the encoder-induced change in GaussianW 2 and panel titles for its Spearman correlation with the corresponding change in Mah-NCM accuracy. Thus each panel asks whether the train–test pairs whose estimated shift changes most after an encoder swap are also the pairs whose detector accuracy changes most. High correlation means the shift estimate is decision-aligned for that encoder pair. Weak correlation meansW 2 is responding to feature-space changes that the detector does not use: ΔW 2 (D train ,D test ;휙 푎 , 휙 푏 )= W (휙 푎 ) 2 (D train ,D test )−W (휙 푏 ) 2 (D train ,D test ) ,(5.3) ΔCA(D test ;휙 푎 , 휙 푏 )= CA (휙 푎 ) (D test )− CA (휙 푏 ) (D test ) .(5.4) Figure 4 shows strong representation dependence. Within a closely related encoder family,CF-224 andCF-384(Park and Owens, 2025) have a modestΔW 2 on average. Across larger backbone changes, such asPE-Core-bigG-14-448(Bolya et al., 2025) versusCF-384(Park and Owens, 2025),ΔW 2 increases by an order of magnitude, especially for real-only datasets. The sensitivity is also uneven. 12 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection Particular prior–test pairs exhibit consistently largerΔW 2 , indicating that some distribution shifts are more representation-fragile. A weak association betweenΔW 2 andΔCAimplies that global distributional distances can change under encoder re-parameterizations that do not materially affect the discriminative geometry used by Mah-NCM. For example, anisotropic rescaling can inflate Wasserstein distances while leaving the effective decision geometry largely intact. Percept-Lens therefore measures generalization at the level of complete detection systems (training prior×encoder×classifier), and the representation axis is not interchangeable. Any claim that usesW 2 to argue for or against a training prior must therefore be stated as representation-conditioned. Robust conclusions should rely on patterns that persist across encoders (e.g., rank-consistent prior ordering or decision-aligned shift measures), rather than absoluteW 2 values in a single feature space. Practical reporting checklist. These experiments suggest a minimal audit for future AIGI detector papers. Authors should report the released head and the best Gaussian rung on the same frozen features and support prior, include per-dataset CA/AUC rather than only macro averages, state the encoder used for any geometric shift metric, and flag non-Gaussian feature regimes using diagnostics such as those in Appendix Tables 23 and 24. This makes head-level OOD claims auditable without treating the Gaussian ladder as a replacement for specialized detectors. 6. Conclusion This paper studies prior-conditioned Gaussian discriminants as practical baselines and diagnostics for AI-generated image detection under joint distribution shift. Using a unified public-data protocol, the ladder is often competitive with trained detector heads under matched priors and encoders, and sometimes exceeds them. We support a matched head audit plus controlled prior/encoder sweeps, not a fully symmetric decomposition of every detector component. 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The computational cost depends on the covariance structure. Isotropic and diagonal heads require only per-dimension statistics (푂(푁퐷)). Full-covariance heads (Mah-NCM/QDA) additionally estimate a퐷× 퐷covariance (푂(푁퐷 2 )) and invert or solve linear systems (푂(퐷 3 )), which can be non-trivial for very large퐷or very large푁. However, this cost is paid once per (prior, encoder) pair and does not scale with the number of training epochs. In contrast, gradient-based heads typically require many passes over the data and introduce additional variance from stochastic optimization and hyperparameter choices. For our purposes, this simplicity is a feature. The Gaussian ladder provides a controlled baseline and diagnostic, while its one-shot fitting reduces optimization confounds and makes head comparisons easier to reproduce. B. Proofs of Theoretical Propositions We provide formal derivations for the propositions presented in the theoretical framework Section 4.1. We adopt the notation defined in the main text. B.1. Proof of Proposition 1 (Bayes-Optimal Classifier under Gaussian Assumption) Proposition 5. If the class-conditional densities are Gaussian,푝(푧 | 푦= 푐) ∼N(휇 푐 ,Σ 푐 ), and the class priors are equal,푃(푦=0)= 푃(푦=1)= 1 2 , the decision rule that minimizes the probability of error (the Bayes-optimal rule) is given by Quadratic Discriminant Analysis (QDA). Proof.The Bayes-optimal decision rule minimizes the probability of misclassification by assigning a feature vector푧to the class푐with the maximum a posteriori (MAP) probability,푃(푦= 푐|푧). For a binary classification task, this means that we assign푧to class 1 if푃(푦=1|푧) > 푃(푦=0|푧)and to class 0 otherwise. Formulating the Decision Rule. Using Bayes’ theorem, the posterior probability is푃(푦= 푐|푧)= 푝(푧|푦=푐)푃(푦=푐) 푝(푧) . The MAP decision rule is therefore: 푝(푧|푦= 1)푃(푦= 1) 푝(푧) > 푝(푧|푦= 0)푃(푦= 0) 푝(푧) (B.1) Since the evidence푝(푧)is a positive common denominator and we assumed that the class priors are equal (푃(푦=1)= 푃(푦=0)= 1 2 ). The decision rule simplifies to a comparison of the class-conditional likelihoods: 푝(푧|푦= 1) > 푝(푧|푦= 0)(B.2) We define the decision function 푔 ∗ (푧) as the log-likelihood ratio: 푔 ∗ (푧)= log 푝(푧|푦= 1)− log 푝(푧|푦= 0)(B.3) The decision rule using the log-likelihood ratio is to classify as class 1 if푔 ∗ (푧) >0 and class 0 otherwise. 21 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection Introducing Gaussian PDF assumption to decision rule. The probability density function (PDF) for a multivariate Gaussian distribution is: 푝(푧|푦= 푐)=N(푧; 휇 푐 ,Σ 푐 )= 1 (2휋) 퐷/2 |Σ 푐 | 1/2 exp − 1 2 (푧− 휇 푐 ) ⊤ Σ −1 푐 (푧− 휇 푐 ) (B.4) The corresponding log-likelihood for class 푐 is: log 푝(푧|푦= 푐)=− 퐷 2 log(2휋)− 1 2 log|Σ 푐 |− 1 2 (푧− 휇 푐 ) ⊤ Σ −1 푐 (푧− 휇 푐 )(B.5) Using this expression in the decision function푔 ∗ (푧)Equation (B.3), we convert our decision rule into an approximation using Gaussian parameters after simplification. 푔 ∗ (푧) ∝ (푧− 휇 0 ) ⊤ Σ −1 0 (푧− 휇 0 )−(푧− 휇 1 ) ⊤ Σ −1 1 (푧− 휇 1 )+ log |Σ 0 | |Σ 1 | (B.6) This is the discriminant function for Quadratic Discriminant Analysis (QDA), which is therefore Bayes-optimal under the stated Gaussian assumption. B.2. Proof of Proposition 2 (Optimality under Homoscedasticity) Proposition 6. If the classes are additionally assumed to be homoscedastic (i.e., they share a common covariance matrixΣ 0 =Σ 1 =Σ 푝 ), the decision rule that minimizes the probability of error (the Bayes- optimal rule) is given by Mahalanobis Nearest Centroid Matching (Mah-NCM). Proof.We begin with the Bayes-optimal QDA decision function derived above Equation (B.6) and apply the homoscedasticity assumptionΣ 0 =Σ 1 =Σ 푝 to the decision function Equation (B.6) and after simplifications of the quadratic forms, the decision rule becomes of the form: 푔 ∗ (푧) ∝ (푧− 휇 0 ) ⊤ Σ −1 푝 (푧− 휇 0 )−(푧− 휇 1 ) ⊤ Σ −1 푝 (푧− 휇 1 )(B.7) ∝ 푧 ⊤ Σ −1 푝 푧− 2휇 ⊤ 0 Σ −1 푝 푧+ 휇 ⊤ 0 Σ −1 푝 휇 0 − 푧 ⊤ Σ −1 푝 푧− 2휇 ⊤ 1 Σ −1 푝 푧+ 휇 ⊤ 1 Σ −1 푝 휇 1 (B.8) ∝ 2휇 ⊤ 1 Σ −1 푝 푧− 2휇 ⊤ 0 Σ −1 푝 푧+ 휇 ⊤ 0 Σ −1 푝 휇 0 − 휇 ⊤ 1 Σ −1 푝 휇 1 (B.9) ∝ 2(휇 1 − 휇 0 ) ⊤ Σ −1 푝 푧−(휇 ⊤ 1 Σ −1 푝 휇 1 − 휇 ⊤ 0 Σ −1 푝 휇 0 )(B.10) ∝ 2(휇 1 − 휇 0 ) ⊤ Σ −1 푝 푧−(휇 1 − 휇 0 ) ⊤ Σ −1 푝 (휇 1 + 휇 0 )(B.11) Note that this assumption of homoscedasticityΣ 0 =Σ 1 =Σ 푝 linearizes the decision boundary: 푔 ∗ (푧) ∝푤 ⊤ 푧+ 푏(B.12) where 푤=Σ −1 푝 (휇 1 − 휇 0 )(B.13) 푏=− 1 2 (휇 1 + 휇 0 ) ⊤ 푤=− 1 2 (휇 1 + 휇 0 ) ⊤ Σ −1 푝 (휇 1 − 휇 0 )(B.14) This is the discriminant function for Mahalanobis Nearest Centroid Matching (Mah-NCM), which is therefore Bayes-optimal under the stated homoscedastic Gaussian assumption. 22 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection B.3. Proof Sketch for Proposition 3 (Performance Stability under Bounded Drift) Proposition 7. Assume a homoscedastic classifier with shared covarianceΣand equal priors. If the statistical drift between the training and testing distributions is bounded by∥휇 test 푐 − 휇 train 푐 ∥ 2 ≤ 휖 휇 and ∥Σ test −Σ train ∥ 퐹 ≤ 휖 Σ , then |AUC test − AUC train | ≤ 퐿(휖 휇 + 휖 Σ ). Proof Sketch. A full proof requires extensive details from perturbation theory. We provide a rigorous sketch outlining the main logical steps. Expressing AUC as a function of statistical parameters. For a linear classifier with weight vector 푤, the AUC is the probability that a randomly drawn positive sample scores higher than a randomly drawn negative sample:AUC= 푃(푤 ⊤ 푍 1 > 푤 ⊤ 푍 0 ), where푍 푐 ∼N(휇 푐 ,Σ). Let the score difference be the random variable푌= 푤 ⊤ (푍 1 − 푍 0 ). Since푍 1 and푍 0 are independent Gaussian variables, their difference is also Gaussian:푍 1 − 푍 0 ∼N(휇 1 − 휇 0 ,2Σ). Therefore,푌is a scalar Gaussian with mean 피[푌]= 푤 ⊤ (휇 1 − 휇 0 )and varianceVar(푌)= 푤 ⊤ (2Σ)푤. The AUC is푃(푌 >0), which can be expressed using the CDF of the standard normal distribution,Φ: AUC= 푃 푌 − 피[푌] √︁ Var(푌) > −피[푌] √︁ Var(푌) ! =Φ 피[푌] √︁ Var(푌) ! (B.15) Under the homoscedastic Gaussian assumption, for the optimal linear classifier Mahalanobis Nearest Centroid Matching (Mah-NCM) where 푤=Σ −1 (휇 1 − 휇 0 ), this simplifies to: AUC=Φ (휇 1 − 휇 0 ) ⊤ Σ −1 (휇 1 − 휇 0 ) √︁ 2(휇 1 − 휇 0 ) ⊤ Σ −1 Σ −1 (휇 1 − 휇 0 ) ! =Φ √︂ D 휇 2 ! (B.16) This establishes that the AUC is a direct and smooth function of the Fisher marginD 휇 . Establishing Lipschitz Continuity. It remains to show thatAUCis locally Lipschitz. The map is a composition of three parts: 1.The Fisher MarginD 휇 =(휇 1 − 휇 0 ) ⊤ Σ −1 (휇 1 − 휇 0 )is a smooth (infinitely differentiable) function of its arguments as long asΣis invertible. (Note that all the training datasets we used in the experiments made this assumption of invertibleΣvalid by ensuring푛 >> 푑, future works can explore the shrinkageΣusing Ledoit-Wolf Shrinkage when training sets are of form푛 << 푑, ensuringΣ is invertible). 2. The square root function, which is locally Lipschitz in (0,∞). 3. The standard normal CDFΦ(푥), which is globally Lipschitz because its derivative (the normal PDF) is bounded by 1/ √ 2휋. Since the composition of local Lipschitz functions is locally Lipschitz, the overall function퐴푈퐶is locally Lipschitz. Deriving the bounds on deviation. By the definition of local Lipschitz continuity, for small perturbations in the arguments, the change in the function’s value is bounded by a constant times the magnitude of the perturbation. Therefore, for perturbations bounded by 휖 휇 and 휖 Σ , we have |AUC test − AUC train |=|퐻(휇 test ,Σ test )− 퐻(휇 train ,Σ train )| ≤ 퐿·(∥휇 test − 휇 train ∥+∥Σ test −Σ train ∥) (B.17) This can be expressed as|AUC test − AUC train | ≤ 퐿 1 휖 휇 + 퐿 2 휖 Σ ≤ 퐿(휖 휇 + 휖 Σ ), where퐿= max(퐿 1 , 퐿 2 ). The Lipschitz constant퐿depends on the local derivatives of퐻, which are functions of the training parameters, critically including the spectral norm of the inverse covariance, ∥Σ −1 ∥ 2 . 23 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection B.4. Proof of Proposition 4 (Stability of the Fisher Margin under Distributional Drift) Proposition 8. Assume that both the training and testing domains are characterized by homoscedastic Gaussian parameters(휇 train 푐 ,Σ train 푝 ) and(휇 test 푐 ,Σ test 푝 ) , respectively. If the distributional drift is bounded such that∥훿 test − 훿 train ∥ 2 ≤ 휖and∥Σ test 푝 −Σ train 푝 ∥ 퐹 ≤ 휂, where훿= 휇 1 − 휇 0 , then the absolute change in the Fisher MarginD 휇 is bounded, to a first order, by |D test 휇 −D train 휇 | ≤ 2∥(Σ train 푝 ) −1 ∥ 2 ∥훿 train ∥ 2 휖+ 푂(휂). Proof.We analyze the change in Fisher MarginD 휇 = 훿 ⊤ Σ −1 푝 훿 under small perturbations. We define perturbations asΔ훿= 훿 test − 훿 train andΔΣ 푝 =Σ test 푝 −Σ train 푝 , with norms bounded by∥Δ훿∥ 2 ≤ 휖and ∥ΔΣ 푝 ∥ 퐹 ≤ 휂. First-Order Taylor Expansion. On expandingD 휇 around the training parameters(훿 train ,Σ train 푝 ), in first order, the change is given by the total derivative: ΔD 휇 =D test 휇 −D train 휇 ≈ ∇ 훿 D 휇 ⊤ Δ훿+⟨∇ Σ 푝 D 휇 ,ΔΣ 푝 ⟩ 퐹 (B.18) where the gradients are evaluated at the training parameters. Gradient with respect to 훿. ∇ 훿 D 휇 = 2Σ −1 푝 훿(B.19) Gradient with respect toΣ 푝 . 푑D 휇 =(푑훿 ⊤ )Σ −1 푝 훿+ 훿 ⊤ Σ −1 푝 (푑훿)+ 훿 ⊤ (푑Σ −1 푝 )훿(B.20) = 2훿 ⊤ Σ −1 푝 푑훿− 훿 ⊤ Σ −1 푝 (푑Σ 푝 )Σ −1 푝 훿(B.21) = Tr 2훿 ⊤ Σ −1 푝 푑훿 − Tr 훿 ⊤ Σ −1 푝 (푑Σ 푝 )Σ −1 푝 훿 (B.22) = Tr 2훿 ⊤ Σ −1 푝 푑훿 − Tr Σ −1 푝 훿 ⊤ Σ −1 푝 푑Σ 푝 (B.23) From the definition of the Frobenius inner product,⟨퐴, 퐵⟩ 퐹 = Tr(퐴 ⊤ 퐵), the gradient with respect toΣ 푝 is: ∇ Σ 푝 D 휇 =− Σ −1 푝 훿 ⊤ Σ −1 푝 ⊤ =−Σ −1 푝 훿 ⊤ Σ −1 푝 (B.24) sinceΣ 푝 is symmetric. Deriving the bound on the magnitude of the change. Using the triangle inequality on the first- order expansion Equation (B.18): |ΔD 휇 | ≤ ∇ 훿 D 휇 ⊤ Δ훿 + ⟨∇ Σ 푝 D 휇 ,ΔΣ 푝 ⟩ 퐹 (B.25) We bound each term separately: Mean Drift Term. By the Cauchy-Schwarz inequality: 2(Σ train 푝 ) −1 훿 train ⊤ Δ훿 ≤ ∥2(Σ train 푝 ) −1 훿 train ∥ 2 ∥Δ훿∥ 2 ≤ 2∥(Σ train 푝 ) −1 ∥ 2 ∥훿 train ∥ 2 휖 where ∥·∥ 2 is the spectral norm for matrices and the Euclidean norm for vectors. 24 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection Covariance Drift Term. Using the property of the Frobenius inner product, |⟨퐴, 퐵⟩ 퐹 | ≤ ∥퐴∥ 퐹 ∥퐵∥ 퐹 : ⟨∇ Σ 푝 D 휇 ,ΔΣ 푝 ⟩ 퐹 ≤ ∥∇ Σ 푝 D 휇 ∥ 퐹 ∥ΔΣ 푝 ∥ 퐹 ≤ 퐶· 휂= 푂(휂) where 퐶=∥(Σ train 푝 ) −1 훿 train (훿 train ) ⊤ (Σ train 푝 ) −1 ∥ 퐹 is a constant determined by the training distribution. Combining the bounds for both terms yields: D test 휇 −D train 휇 ≤ 2∥(Σ train 푝 ) −1 ∥ 2 ∥훿 train ∥ 2 휖+ 푂(휂)(B.26) This shows that the change in the Fisher MarginD 휇 is controlled, to a first order, by the magnitude of the drift in the class statistics. C. Analytical Forms of the Gaussian Discriminant Ladder For each rung, we estimate class means휇 푐 and (optionally) covariance matrices from a labeled support set in the training prior. Given a test feature푧, the heads produce unnormalized class scores푔 푐 (푧)and predictˆ푦(푧)= arg max 푐∈0,1 푔 푐 (푧). The score functions used in Table 1 are listed below. (Additive constants shared across classes are omitted.) Class priors. To avoid confounding head comparisons with class-imbalance in the support prior, we use uniform class priors by default (휋 0 = 휋 1 = 1 2 ), so anylog휋 푐 terms are class-independent and may be dropped. When we report results with empirical priors,휋 푐 denotes the support-set class frequency and is stated explicitly. Balanced evaluation metrics (e.g., balanced accuracy) do not in general remove prior-induced offsets in the decision rule. Euc-NCM (isotropic, shared covariance). 푔 푐 (푧)=−∥푧− 휇 푐 ∥ 2 2 .(C.1) Cos-NCM (cosine similarity). 푔 푐 (푧)= 푧 ∥푧∥ 2 , 휇 푐 ∥휇 푐 ∥ 2 .(C.2) GNB (diagonal covariance). LetΣ 푐 = diag(휎 2 푐 ). 푔 푐 (푧)=− 1 2 푑 ∑︁ 푗=1 (푧 푗 − 휇 푐,푗 ) 2 휎 2 푐,푗 + log휎 2 푐,푗 ! + log휋 푐 .(C.3) Mah-NCM / LDA (shared full covariance). LetΣ 0 =Σ 1 =Σ. 푔 푐 (푧)= 푧 ⊤ Σ −1 휇 푐 − 1 2 휇 ⊤ 푐 Σ −1 휇 푐 + log휋 푐 .(C.4) QDA (class-specific full covariance). 푔 푐 (푧)=− 1 2 (푧− 휇 푐 ) ⊤ Σ −1 푐 (푧− 휇 푐 )− 1 2 log det(Σ 푐 )+ log휋 푐 .(C.5) (With the default uniform priors used in this paper,log휋 푐 is constant across푐and is omitted in implementation.) 25 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection Table 8|Summary of training priors used for conditioning. We list the public datasets used as training priors in our experiments and report the number of real and synthetic images available in the version used by our pipeline.♣indicates that counts correspond to the publicly available subset used in our preprocessing and may differ from the full dataset described in the original source due to corrupted images in the original source. Training DatasetTotal ImagesReal Synthetic CNNSpot (Wang et al., 2020)720,119360,059360,060 GenImage♣ (Zhu et al., 2023)2,254,762 1,116,779 1,137,983 GenImage-SDv1 (Zhu et al., 2023)323,997162,000161,997 DRCT-2M♣ (Chen et al., 2024)2,247,453118,287 2,129,166 DRCT-SDv1 (Chen et al., 2024)473,148118,287354,861 DRCT-SDv2 (Chen et al., 2024)473,148118,287354,861 CommunityForensics♣ (Park and Owens, 2025)4,386,820 1,678,386 2,708,434 ELSA-D3♣ (Baraldi et al., 2025)8,417,550 1,683,511 6,734,039 D. Details about existing datasets in our Percept-Lens evaluation suite The following tables list the datasets used for training (Table 8) and evaluation (Table 9) to make the experimental setup reproducible. Percept-Lens uses public datasets, leaves support priors out of evaluation, and combines generator style, source-domain, and post-processing shifts rather than a single generator-only shift. Covariance estimation and numerical stability. For full-covariance rules (Mah-NCM/QDA), covariance inversion in high-dimensional feature spaces can be ill-conditioned, especially in low-shot regimes. We therefore regularize covariance estimates before computingΣ −1 andlog det(Σ). Concretely, we use an empirical covariance estimate with diagonal loading, b Σ← b Σ+ 휀퐼 , and compute inverses via a numerically stable pseudo-inverse (small singular values truncated) to avoid catastrophic failures when b Σis nearly singular. Log-determinants are computed from the (clipped) spectrum of b Σto guarantee finite values. All priors and encoders are evaluated with the same estimator and regularization hyperparameters to avoid confounding. We use standard regularization (shrinkage estimators such as Ledoit–Wolf, plus diagonal loading 휖퐼) before computingΣ −1 and log-determinants, when computing the covariances for data-efficiency results in Tables 7 and 22. This is because under extreme data shrinkage, we enter the푁 < 퐷regime (number of samples smaller than feature dimension), where empirical covariance estimates are unstable. All priors and backbones are evaluated with the same estimator to avoid confounding. Table 9|Summary of Percept-Lens evaluation datasets. We list the public datasets used to evaluate generalization and report the number of real and synthetic images.♦indicates that we evaluate on all officially released subsets/variants provided by the source; when a dataset provides multiple transformations of the same underlying image, we treat each transformation as a separate evaluation subset and do not interpret the resulting counts as independent samples. Evaluation DatasetTotal ImagesRealSynthetic Out-of-Distribution Existing Datasets with only Real Images Unsplash (Lite Subset) (uns)24,96924,969— InstagramImagesWithCaptions (ins)34,92734,927— Anime Faces Dataset (Churchill and Chao, 2019)63,56563,565— Anime Images (Banana_Leopard, 2023)82,97582,975— CelebA-Spoof♦ (Zhang et al., 2020)561,575561,575— Continued on next page 26 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection Evaluation DatasetTotal ImagesRealSynthetic Out-of-Distribution Existing Datasets with only Synthetic Images AGIQA-1k (Zhang et al., 2023)1,080—1,080 AGIQA-3k (Li et al., 2024)2,982—2,982 SPAI (Karageorgiou et al., 2025)3,638—3,638 SynthBuster Extended (Bammey, 2024; Guillaro et al., 2025) 11,003—11,003 SynthScars (Kang et al., 2025)12,182—12,182 GigaGAN (Kang et al., 2023)170,000—170,000 LatentDiffusion (Corvi et al., 2023)216,000—216,000 MidJourneyV6 (ter)519,849—519,849 Co-Spy-Bench (Cheng et al., 2025)550,000—550,000 Dalle3 (Egan et al., 2024)1,193,805—1,193,805 Out-of-Distribution Existing Datasets with both Real and Synthetic Images FourierSpectrumDiscrepancies (Dzanic et al., 2020)901575 FakeInversion (Cazenavette et al., 2024)1,300650650 UniversalFakeDetect (Ojha et al., 2023)10,0002,0008,000 Dalle Recognition Dataset (Koliha, 2024)21,6353,78017,855 Chameleon (Yan et al., 2024)26,03314,86311,170 AIGI-Detection-Quality-Paradox (Xiao et al., 2025)27,8643,86424,000 DiTFake (Li et al., 2025b)30,00015,00015,000 Diffusion1kSteps (Tan et al., 2024)35,99218,00017,992 GANGen-Detection (Chuangchuang Tan, 2024)36,00018,00018,000 RobustLDM (Rajan et al., 2024)42,7526,00036,752 RealRobustBench (Li et al., 2025a)53,99926,99927,000 LDMFakeDetect (Rajan and Lee, 2025)61,3526,00055,352 DIF (Sinitsa and Fried, 2024)75,34437,67237,672 ForenSynths (Wang et al., 2020)90,32945,16945,160 DNF-TestSet (Zhang and Xu, 2025)91,2677,00084,267 DeepFakeFace (Song et al., 2023)120,00030,00090,000 AIGCDetectBench (Zhong et al., 2024)152,59776,29876,299 AIGI-Holmes (Zhou et al., 2025b)164,99683,85081,146 AI-Artwork (Kholy, 2024)271,99381,444190,549 DiffusionForensics (Wang et al., 2023)313,36886,000227,368 B-Free (Guillaro et al., 2025)361,58452,482309,102 LASTED (Wu et al., 2025a)367,533136,287231,246 AIGIBench (Li et al., 2025c)520,826260,514260,312 DeepFakeBench (Yan et al., 2023)803,99170,998732,993 Percept-Lens Evaluation Suite7,129,3951,850,8965,278,499 E. Extended Investigation of Generalization with Percept-Lens suite 27 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection Table 10|Closed-form Gaussian discriminants versus released AI-generated image detector heads under matched (prior, encoder) conditions. Mean class accuracyCA(dataset-wise balanced accuracy where defined; Section 5.1), macro- averaged across Percept-Lens evaluation datasets. For each released detector checkpoint, we report (i) the released decision head (Out-of-the-Shelf) and (i) closed-form baselines fitted on the same frozen encoder features using the corresponding public training prior: Euc-NCM (Wu et al., 2025b) and the Gaussian ladder. (Parentheses indicate the training subset reported by the original work when applicable.) Detection ModelOut-of-the-Shelf Euc-NCM (Wu et al., 2025b) Cos-NCMGNB Mah-NCMQDA Trained with GenImage (Zhu et al., 2023) (Diffusion Model Images based on ImageNet-1k Dataset) DRCT-ConvNeXt (Full GenImage) (Chen et al., 2024)46.92%65.44%64.67%58.21%65.54%61.19% Trained with DRCT-2M (Chen et al., 2024) (Stable Diffusion Model Images based on COCO Dataset) DRCT-ConvNeXt (DRCT-SDv1) (Chen et al., 2024)46.92%57.14%57.64%57.79%52.66%59.93% DRCT-ConvNeXt (DRCT-SDv2) (Chen et al., 2024)50.60%62.02%60.95%61.82%60.69%61.20% Trained with ELSA-D3 (Baraldi et al., 2025) (Diffusion Model Images based on LAION-400M Dataset) CoDE-SVM (ELSA-D3) (Baraldi et al., 2025)36.01%63.63%62.70%65.98%66.15%64.00% CoDE-Linear (ELSA-D3) (Baraldi et al., 2025)62.34%63.63%62.70%65.98%66.15%64.00% Table 11|Encoder scaling under a fixed prior: representation choice strongly affects transfer. Mean class accuracy CA(macro-averaged across Percept-Lens evaluation datasets) for Gaussian discriminant heads conditioned on the same CommunityForensicstraining prior (Park and Owens, 2025), using frozen CLIP encoders of increasing capacity pretrained and available in OpenCLIP (Ilharco et al., 2021). Only the head is changed. No detector fine-tuning is performed. Frozen EncodersEuc-NCM (Wu et al., 2025b) Cos-NCMGNB Mah-NCM QDA convnext_base-laion400m_s13b_b51k65.64% 65.00% 65.99% 67.96% 62.27% convnext_base_w-laion_aesthetic_s13b_b82k67.26% 67.25% 66.97% 73.32% 64.98% convnext_base_w-laion2b_s13b_b82k_augreg67.64% 67.66% 68.20% 73.43% 66.93% convnext_base_w-laion2b_s13b_b82k66.95% 66.91% 66.00% 74.43% 63.32% convnext_base_w_320-laion_aesthetic_s13b_b82k67.22% 67.16% 66.88% 72.75% 64.89% convnext_base_w_320-laion_aesthetic_s13b_b82k_augreg67.33% 66.99% 66.43% 73.06% 64.52% convnext_large_d-laion2b_s26b_b102k_augreg68.99% 68.73% 68.58% 74.81% 67.48% convnext_large_d_320-laion2b_s29b_b131k_ft69.11% 68.30% 68.13% 74.87% 67.91% convnext_large_d_320-laion2b_s29b_b131k_ft_soup68.49% 67.77% 67.25% 73.71% 66.45% convnext_xxlarge-laion2b_s34b_b82k_augreg71.61% 70.73% 72.14% 78.76% 71.70% convnext_xxlarge-laion2b_s34b_b82k_augreg_soup71.50% 70.77% 71.89% 79.34% 71.44% convnext_xxlarge-laion2b_s34b_b82k_augreg_rewind71.60% 70.75% 71.94% 79.41% 71.34% ViT-B-16-datacomp_xl_s13b_b90k67.26% 67.57% 67.48% 72.27% 64.20% ViT-B-32-datacomp_xl_s13b_b90k65.05% 66.13% 66.19% 72.23% 62.56% ViT-L-14-datacomp_xl_s13b_b90k64.83% 64.73% 63.74% 66.39% 64.68% ViT-L-14-laion400m_e3265.93% 65.14% 65.64% 71.90% 63.39% ViT-L-14-laion400m_e3165.91% 65.19% 65.61% 71.92% 63.40% ViT-L-14-laion2b_s32b_b82k66.67% 66.33% 65.46% 73.06% 62.95% ViT-L-14-commonpool_xl_clip_s13b_b90k67.31% 69.42% 68.06% 74.60% 65.43% ViT-L-14-commonpool_xl_laion_s13b_b90k70.22% 70.81% 71.09% 75.13% 66.23% ViT-L-14-quickgelu-metaclip_400m66.73% 70.09% 71.15% 75.74% 67.72% ViT-L-14-quickgelu-metaclip_fullcc69.45% 72.62% 72.65% 76.07% 68.22% ViT-L-14-quickgelu-dfn2b65.06% 70.29% 68.69% 76.21% 66.36% ViT-L-14-dfn2b_s39b65.86% 70.70% 69.92% 76.24% 67.99% ViT-L-14-commonpool_xl_s13b_b90k67.34% 70.13% 72.37% 78.77% 69.05% ViT-L-14-336-quickgelu-openai68.20% 70.42% 72.33% 78.85% 71.36% ViT-H-14-quickgelu-metaclip_fullcc71.58% 74.11% 73.68% 77.83% 69.08% ViT-H-14-quickgelu-dfn5b70.80% 74.92% 74.00% 79.02% 72.82% ViT-H-14-worldwide-quickgelu-metaclip2_worldwide79.15% 81.57% 84.01% 84.20% 76.89% ViT-H-14-378-quickgelu-dfn5b72.12% 76.05% 74.75% 78.36% 74.02% ViT-H-14-worldwide-378-metaclip2_worldwide82.10% 84.81% 86.86%85.53% 80.68% ViT-bigG-14-quickgelu-metaclip_fullcc72.62% 76.43% 76.65% 79.56% 72.17% ViT-bigG-14-worldwide-metaclip2_worldwide85.79% 85.72% 86.16% 87.36% 80.28% ViT-bigG-14-worldwide-378-metaclip2_worldwide88.65% 88.94% 89.01% 89.28% 83.77% Continued on next page 28 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection Frozen EncodersEuc-NCM (Wu et al., 2025b) Cos-NCMGNB Mah-NCMQDA Table 12|Pretraining objective affects transfer even without detector training. Mean class accuracyCA(macro-averaged across Percept-Lens evaluation datasets) for Gaussian discriminant heads conditioned on the sameCommunityForensics training prior (Park and Owens, 2025), using frozen encoders trained with different objectives. Frozen EncodersEuc-NCM (Wu et al., 2025b) Cos-NCMGNB Mah-NCMQDA CLIP-RoBERTa63.81%64.64%63.87%69.10%62.00% CLIP-XLM-RoBERTa-Base63.13%64.34%64.47%72.20%62.34% MAE-Base58.35%58.13%59.37%68.46%63.74% MAE-Large59.56%59.72%62.39%68.39%60.79% BEiT-Base57.81%57.69%58.30%59.57%52.12% SigLIP-so400m56.30%57.78%58.55%64.02%59.01% SigLIP2-Base-22458.37%58.37%58.34%61.78%55.37% SigLIP2-Base-51258.58%58.79%58.68%63.28%56.59% SigLIP2-Large-51256.10%56.03%56.92%69.30%60.75% coca_ViT-L-14]66.90%67.01%64.00%70.81%63.43% coca_ViT-L-14-mscoco_finetuned62.06%61.51%62.81%69.50%64.80% EVA01-g-14-laion400m_s11b_b41k69.54%68.51%66.61%76.74%62.44% EVA01-g-14-plus-merged2b_s11b_b114k69.56%71.17%70.12%78.72%67.08% EVA02-B-16-merged2b_s8b_b131k63.75%63.08%64.53%71.38%60.78% EVA02-L-14-merged2b_s4b_b131k66.64%67.16%67.08%72.81%63.06% CLIPA-ViT-L-1465.69%66.90%66.31%76.08%68.51% CLIPA-ViT-L-14-33665.42%66.92%67.08%76.25%69.25% CLIPA-ViT-H-1467.23%68.18%69.12%79.17%70.58% CLIPA-ViT-bigG-14-33668.66%70.67%72.72%80.27%73.00% nllb-clip-large-v170.73%69.71%70.61%77.65%65.80% nllb-clip-large-siglip-v159.72%59.48%59.24%67.55%63.01% nllb-clip-large-siglip-mrl59.21%59.02%59.34%68.23%62.47% MobileCLIP2-L-14-dfndr2b66.48%69.43%68.33%75.12%65.68% ViTamin-S63.22%64.43%63.51%67.72%65.09% ViTamin-S-LTT64.41%65.18%64.86%68.38%65.07% ViTamin-B62.75%64.25%64.21%70.75%65.65% ViTamin-B-LTT64.97%65.60%64.85%72.40%67.23% ViTamin-L67.94%68.42%69.08%76.64%69.57% ViTamin-L-25667.57%68.19%68.07%75.90%70.56% ViTamin-L-33667.36%68.36%67.76%76.18%69.49% ViTamin-L-38474.43%73.08%76.17%76.35%65.83% ViTamin-L270.11%69.25%70.75%77.03%70.16% ViTamin-L2-25670.50%69.74%70.01%77.18%71.64% ViTamin-L2-33670.42%69.62%69.72%77.07%69.77% ViTamin-L2-38470.53%69.82%68.51%75.64%66.00% ViTamin-XL-25671.25%70.35%71.62%80.74%71.36% ViTamin-XL-33671.63%71.10%71.54%79.92%70.52% ViTamin-XL-38471.56%70.91%72.49%79.82%71.52% DINOv2-Small62.02%61.77%60.99%66.63%60.17% DINOv2-Base63.79%64.06%62.08%68.45%59.43% Continued on next page 29 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection Frozen EncodersEuc-NCM (Wu et al., 2025b) Cos-NCMGNB Mah-NCMQDA DINOv2-Large63.03%62.78%62.29%70.17%59.34% DINOv3-ConvNeXt-Tiny61.14%62.31%59.97%65.68%59.85% DINOv3-ConvNeXt-Small61.70%61.98%59.60%65.65%60.30% DINOv3-ConvNeXt-Base64.54%63.46%61.39%70.34%62.68% DINOv3-ConvNeXt-Large69.32%67.70%69.02%74.15%66.77% DINOv3-ViT-S-1664.52%64.26%64.18%66.92%61.55% DINOv3-ViT-S-16+64.46%64.03%63.78%67.35%63.35% DINOv3-ViT-B-1668.83%66.69%69.67%76.08%65.32% DINOv3-ViT-L-1679.34%74.74%79.32%83.31%71.37% DINOv3-ViT-H-16+82.13%79.58%80.99%86.22%77.52% PE-Core-T-16-384-meta54.56%54.78%54.54%63.27%55.27% PE-Core-S-16-384-meta64.32%63.01%64.63%68.13%63.69% PE-Core-B-16-meta67.25%67.02%68.19%73.08%66.10% PE-Core-L-14-336-meta81.78%80.77%84.76%89.51%78.76% Table 10 extends the matched (prior, encoder) audit to additional ConvNeXt checkpoints (Chen et al., 2024) and alternative CoDE heads (Baraldi et al., 2025). The pattern remains mostly unfavorable to the released heads. On the same frozen ConvNeXt representation, replacing the released head with a closed-form Gaussian rule yields CA gains for all three DRCT checkpoints: from 46.92% to 65.54% for the fullGenImagemodel, from 46.92% to 59.93% forDRCT-SDv1, and from 50.60% to 62.02% forDRCT-SDv2. The CoDE comparison isolates the head effect more directly.CoDE-Linearand CoDE-SVMinduce identical closed-form baselines because they share the same frozen encoder and the same support prior, yet their released heads differ sharply (62.34% versus 36.01%). Representation quality alone cannot explain this gap. The comparison instead points to head sensitivity on top of a fixed representation. As throughout the paper, this remains a post hoc swap on the final released representation, not a replay of the original training pipeline. The conservative conclusion is therefore that the released head does not always recover separability already present in the final encoder, not that end-to-end training is unnecessary. Table 11 shows that the encoder effect is not confined to the smaller OpenAI sweep in the main text. Under the sameCommunityForensicsprior and with no detector fine-tuning, the best CA rises from67.96%forconvnext_base-laion400m_s13b_b51kto79.41%for convnext_xxlarge-laion2b_s34b_b82k_augreg_rewind. The larger ViT family exhibits a wider spread, from 66.39% to 89.28%. This spread is larger than many method-level gains reported in the detector literature, making head-only comparisons difficult to interpret unless encoder choice is controlled. Mah-NCM is the modal winner across rows, but the pattern is not universal. On the strongest encoders the margin often collapses, and in isolated cases another Gaussian rule is competitive or better. Any claim of universal Mahalanobis dominance would therefore be overstated. Table 12 further reinforces the representation-centric reading. The best CA ranges from 59.57% for BeiT-Baseto 89.51% forPE-Core-L-14-336-meta, whileDINOv3-ViTH16plusalready reaches 86.22% without any detector-specific fine-tuning. These gaps are large enough that they should not be treated as marginal implementation details. At the same time, this table should not be over-interpreted as a clean causal statement about a single pretraining objective, because objective, scale, data, and architecture all vary together. The supported claim is narrower. The choice of frozen encoder feature space is a first-order determinant of transfer, and a simple moment-based head on a strong encoder can outperform a specialized detector head trained on a weaker one. Overall, the appendix supports a 30 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection system-level conclusion rather than an algorithmic one. Cross-dataset AIGI detection depends strongly on the joint choice of support prior and representation, while the downstream head often contributes less than its standalone presentation suggests. Table 13|QuickGELU versus GELU in otherwise matched encoders. Mean class accuracyCA(macro-averaged across Percept-Lens evaluation datasets) for Gaussian discriminant heads conditioned on the sameCommunityForensicstraining prior (Park and Owens, 2025), using frozen encoders that differ primarily in whether QuickGELU is used. Frozen EncodersEuc-NCM (Wu et al., 2025b) Cos-NCMGNB Mah-NCM QDA ViT-B-16-openai63.39% 64.66% 64.98%73.19% 64.65% ViT-B-16-quickgelu-openai64.66% 64.65% 66.37% 74.18% 65.70% ViT-B-32-openai63.44% 63.95% 64.34%69.07% 62.20% ViT-B-32-quickgelu-openai64.53% 64.25% 64.83% 70.61% 62.81% ViT-L-14-openai64.19% 66.96% 68.37%76.87% 69.02% ViT-L-14-quickgelu-openai66.18% 68.44% 69.79% 76.96% 68.87% ViT-L-14-336-openai66.33% 69.05% 70.47% 78.89% 71.14% ViT-L-14-336-quickgelu-openai68.20% 70.42% 72.33%78.85% 71.36% ViT-L-14-metaclip_400m64.85% 69.76% 70.40%74.25% 66.65% ViT-L-14-quickgelu-metaclip_400m66.73% 70.09% 71.15% 75.74% 67.72% ViT-L-14-metaclip_fullcc68.07% 72.22% 72.81%75.76% 67.51% ViT-L-14-quickgelu-metaclip_fullcc69.45% 72.62% 72.65% 76.07% 68.22% ViT-L-14-dfn2b66.91% 71.24% 70.16%75.83% 66.52% ViT-L-14-quickgelu-dfn2b65.06% 70.29% 68.69% 76.21% 66.36% ViT-H-14-worldwide-metaclip2_worldwide78.59% 80.28% 82.89%83.59% 76.55% ViT-H-14-worldwide-quickgelu-metaclip2_worldwide79.15% 81.57% 84.01% 84.20% 76.89% ViT-H-14-378-dfn5b73.28% 74.43% 74.08% 78.43% 72.76% ViT-H-14-378-quickgelu-dfn5b72.12% 76.05% 74.75%78.36% 74.02% Table 13 indicates that activation choice is a secondary factor relative to encoder family and scale. Across most matched pairs, the change in CA is modest, and the sign is not consistent across families. QuickGELU helps several models, but it does not provide a plausible explanation for the much larger performance differences observed across encoder families in Tables 11 and 12. Table 14 shows that the aggregate CA gains are broadly distributed across evaluation datasets rather than being driven by a small subset of low-difficulty benchmarks. Mah-NCM is strongest on many mixed and synthetic-only benchmarks, but the exceptions are informative: QDA is best on CelebA-Spoof(Zhang et al., 2020), GNB is strongest onDiffusionForensics(Wang et al., 2023) andDeepFakeBench(Yan et al., 2023), and cosine or Euclidean rules slightly lead on a small number of synthetic-only datasets such asSPAI(Karageorgiou et al., 2025) andMidJourneyV6(ter). The dataset-level view supports the same restrained conclusion as the averaged tables. Covariance-aware scoring is often useful, but no single Gaussian assumption is uniformly best across all shifts. F.Threshold-Free (AUC) Evaluation on Mixed Datasets in Percept-Lens suite In addition to CA, we report ROC-AUC on the 24 mixed datasets that contain both real and synthetic images (Table 9). AUC is not a universally stronger metric than CA, but it is a cleaner diagnostic of ranking quality because it is threshold-free and excludes one-class datasets. If the gains from the Gaussian ladder were mainly artifacts of a favorable operating point, they should shrink under AUC. In several cases they do not, although the counterexamples also become more informative. Table 15 preserves the central matched-head finding under a calibration-agnostic metric. The size of the improvements suggests that threshold selection alone does not explain the result.CoDE-SVMrises from 0.3061 to 0.7039,DRCT-ConvNeXton fullGenImagefrom 0.4977 to 0.7417,AIDEonCNNSpot from 0.4917 to 0.6787, andAIDEon fullGenImagefrom 0.5389 to 0.7082. These are ranking 31 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection Table 14|Per-dataset class accuracy under a fixed encoder and varying training prior. Class accuracyCA for individual datasets in the Percept-Lens evaluation suite for Gaussian discriminant heads under the fixed frozen PE-Core-bigG-14-448encoder (Bolya et al., 2025) and the sameCommunityForensicssupport prior (Park and Owens, 2025) throughout. Evaluation DatasetEuc-NCM (Wu et al., 2025b) Cos-NCMGNB Mah-NCMQDA Out-of-Distribution Existing Datasets with only Real Images Unsplash (Lite Subset) (uns)24.13% 29.07% 75.56% 99.07% 96.20% InstagramImagesWithCaptions (ins)99.65% 99.40% 99.96%99.96% 99.98% Anime Faces Dataset (Churchill and Chao, 2019)100.00% 100.00% 99.98%98.20% 100.00% Anime Images (Banana_Leopard, 2023)99.95% 99.96% 99.97%99.89% 100.00% CelebA-Spoof (Zhang et al., 2020)73.77% 68.03% 79.56%84.70% 94.55% Out-of-Distribution Existing Datasets with only Synthetic Images AGIQA-1k (Zhang et al., 2023)99.81% 99.91% 98.80% 100.00% 97.41% AGIQA-3k (Li et al., 2024)85.81% 84.51% 75.52% 91.15% 51.84% SPAI (Karageorgiou et al., 2025)97.72% 97.77% 90.82%92.00% 76.58% SynthBuster Extended (Bammey, 2024; Guillaro et al., 2025)99.95% 99.94% 98.52%99.05% 91.43% SynthScars (Kang et al., 2025)79.61% 79.17% 62.32% 91.50% 50.90% GigaGAN (Kang et al., 2023)94.86% 94.33% 90.27%94.31% 92.08% LatentDiffusion (Corvi et al., 2023)98.16% 97.85% 99.16% 99.86% 98.42% MidJourneyV6 (ter)99.51% 99.49% 93.92%96.99% 83.88% Co-Spy-Bench (Cheng et al., 2025)99.66% 99.71% 98.27%99.29% 95.88% Dalle3 (Egan et al., 2024)92.22% 93.28% 42.49% 99.25% 59.02% Out-of-Distribution Existing Datasets with both Real and Synthetic Images FourierSpectrumDiscrepancies (Dzanic et al., 2020)85.33% 86.00% 88.67% 100.00% 97.33% FakeInversion (Cazenavette et al., 2024)85.08% 84.38% 91.38% 99.00% 96.08% UniversalFakeDetect (Ojha et al., 2023)98.06% 98.15% 99.07% 99.56% 97.55% Dalle Recognition Dataset (Koliha, 2024)88.56% 88.55% 86.59% 97.16% 83.96% Chameleon (Yan et al., 2024)79.51% 79.20% 72.03% 90.52% 59.45% AIGI-Detection-Quality-Paradox (Xiao et al., 2025)83.70% 82.56% 92.09% 99.42% 92.71% DiTFake (Li et al., 2025b)92.61% 91.91% 98.28% 99.53% 97.93% Diffusion1kSteps (Tan et al., 2024)81.83% 81.17% 88.27% 93.80% 89.57% GANGen-Detection (Chuangchuang Tan, 2024)81.13% 82.48% 94.21% 98.10% 93.40% RobustLDM (Rajan et al., 2024)89.28% 87.62% 88.01% 98.22% 85.73% RealRobustBench (Li et al., 2025a)77.61% 76.96% 75.28% 95.26% 71.61% LDMFakeDetect (Rajan and Lee, 2025)88.85% 87.18% 88.39% 97.63% 84.54% DIF (Sinitsa and Fried, 2024)89.61% 88.51% 96.86% 98.62% 97.80% ForenSynths (Wang et al., 2020)75.85% 74.99% 84.11% 97.06% 91.78% DNF-TestSet (Zhang and Xu, 2025)98.67% 98.50% 99.43% 99.73% 98.92% DeepFakeFace (Song et al., 2023)59.90% 61.67% 62.08% 76.50% 57.65% AIGCDetectBench (Zhong et al., 2024)92.66% 92.22% 97.02% 98.57% 96.47% AIGI-Holmes (Zhou et al., 2025b)90.72% 89.28% 95.21% 98.97% 95.92% AI-Artwork (Kholy, 2024)88.42% 86.86% 90.20% 95.72% 84.95% DiffusionForensics (Wang et al., 2023)95.10% 95.19% 96.44%91.16% 93.02% B-Free (Guillaro et al., 2025)87.75% 87.79% 85.35%85.78% 85.13% LASTED (Wu et al., 2025a)75.98% 74.74% 80.46% 80.80% 76.27% AIGIBench (Li et al., 2025c)86.55% 85.88% 93.92% 95.21% 92.61% DeepFakeBench (Yan et al., 2023)51.39% 52.10% 54.59%52.40% 51.08% improvements, not merely operating-point adjustments. The table also contains counterexamples, since the releasedCF-224andCF-384heads remain marginally stronger than any closed-form surrogate on AUC. CA and AUC therefore diagnose different failure modes. A head swap can improve thresholded balanced accuracy while leaving global ranking unchanged, or vice versa. The strongest result in this block is obtained without detector fine-tuning:PE-Core-bigG-14-448with Mah-NCM reaches 0.9693 AUC. This is not an apples-to-apples replacement for a released detector with a different backbone, but it shows how quickly the comparison shifts once the encoder feature space itself becomes stronger. 32 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection Table 15|Closed-form Gaussian discriminants versus released AI-generated image detector heads under matched (prior, encoder) conditions. Mean ROC-Area Under CurveAUC(dataset-wise ROC-AUC where defined; Section 5.1), macro-averaged across the 24 mixed datasets in Percept-Lens evaluation datasets. For each released detector checkpoint, we report (i) the released decision head (Out-of-the-Shelf) and (i) closed-form baselines fitted on the same frozen encoder features using the corresponding public training prior: Euc-NCM (Wu et al., 2025b) and the Gaussian ladder. (Parentheses indicate the training subset reported by the original work when applicable.) Detection ModelOut-of-the-Shelf Euc-NCM (Wu et al., 2025b) Cos-NCM GNB Mah-NCMQDA Trained with CNNSpot (Wang et al., 2020) (ProGAN Images based on LSUN Dataset) UnivFD (Ojha et al., 2023)0.70910.69950.6756 0.71450.74540.6994 AIDE (Yan et al., 2024)0.49170.52560.5136 0.52780.67870.6383 Trained with GenImage (Zhu et al., 2023) (Diffusion Model Images based on ImageNet-1k Dataset) AIDE (GenImage-SDv1) (Yan et al., 2024)0.52310.56200.5866 0.57100.68750.5929 Effort (GenImage-SDv1) (Yan et al., 2025)0.77290.79510.8348 0.83390.86350.8196 DRCT-ConvNeXt (Full GenImage) (Chen et al., 2024)0.49770.72700.7304 0.61760.74170.6936 DRCT-UnivFD (Full GenImage) (Chen et al., 2024)0.73680.74880.8083 0.78010.83950.7789 AIDE (Full GenImage) (Yan et al., 2024)0.53890.52400.5662 0.53220.70820.5850 Trained with DRCT-2M (Chen et al., 2024) (Stable Diffusion Model Images based on COCO Dataset) DRCT-ConvNeXt (DRCT-SDv1) (Chen et al., 2024)0.49770.61940.6274 0.62360.59200.6460 DRCT-UnivFD (DRCT-SDv1) (Chen et al., 2024)0.73590.67920.7055 0.70600.73890.7363 DRCT-ConvNeXt (DRCT-SDv2) (Chen et al., 2024)0.52300.65690.6449 0.67040.67860.6542 DRCT-UnivFD (DRCT-SDv2) (Chen et al., 2024)0.73660.67810.6916 0.70220.75270.7244 Trained with ELSA-D3 (Baraldi et al., 2025) or CommunityForensics (Park and Owens, 2025) (Diffusion Model Images based on LAION-400M Dataset) CoDE-SVM (ELSA-D3) (Baraldi et al., 2025)0.30610.6986 0.7039 0.70340.68660.6714 CoDE-Linear (ELSA-D3) (Baraldi et al., 2025)0.70650.69860.7039 0.70340.68660.6714 CoDE-kNN (ELSA-D3) (Baraldi et al., 2025)0.63600.6986 0.7039 0.70340.68660.6714 CF-224 (CommunityForensics) (Park and Owens, 2025)0.91310.87990.9101 0.90070.90930.8826 CF-384 (CommunityForensics) (Park and Owens, 2025)0.93510.88210.9304 0.93270.92830.9320 Frozen image encoder (no detection fine-tuning) PE-Core-bigG-14-448 (Bolya et al., 2025)—0.89480.9309 0.94120.96930.9295 Table 16|Encoder scaling under a fixed prior: representation choice strongly affects transfer. Mean ROC-Area Under Curve AUC (macro-averaged across the 24 mixed datasets in Percept-Lens evaluation datasets) for Gaussian discriminant heads conditioned on the sameCommunityForensicstraining prior (Park and Owens, 2025), using frozen CLIP encoders of increasing capacity pretrained by OpenAI. Only the head is changed. No detector fine-tuning is performed. Frozen EncodersEuc-NCM (Wu et al., 2025b) Cos-NCMGNB Mah-NCMQDA ResNet-50 (Timm, 2024a)0.60660.5682 0.63700.7406 0.5844 ResNet-101 (He et al., 2016)0.59990.5823 0.61570.7194 0.5990 ResNet-50x4 (Timm, 2024c)0.62680.6150 0.64910.7633 0.6031 ResNet-50x16 (Timm, 2024b)0.65190.6358 0.68290.8143 0.6404 ResNet-50x64 (Timm, 2024d)0.68700.6752 0.67980.8345 0.6728 ViT-B/16 (Laion, 2024d)0.63340.5965 0.65510.7823 0.6573 ViT-B/32 (Laion, 2024e)0.60650.5831 0.61310.7147 0.6098 ViT-L/14 (Radford et al., 2021)0.66540.6911 0.71650.8193 0.7051 33 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection Table 17|Encoder scaling under a fixed prior: representation choice strongly affects transfer. Mean ROC-Area Under Curve AUC (macro-averaged across the 24 mixed datasets in Percept-Lens evaluation datasets) for Gaussian discriminant heads conditioned on the sameCommunityForensicstraining prior (Park and Owens, 2025), using frozen CLIP encoders of increasing capacity pretrained and available in OpenCLIP (Ilharco et al., 2021). Only the head is changed. No detector fine-tuning is performed. Frozen EncodersEuc-NCM (Wu et al., 2025b) Cos-NCM GNB Mah-NCM QDA convnext_base-laion400m_s13b_b51k0.62880.6177 0.64860.7076 0.6254 convnext_base_w-laion_aesthetic_s13b_b82k0.68200.6733 0.70280.7791 0.6491 convnext_base_w-laion2b_s13b_b82k_augreg0.67750.6765 0.69400.8036 0.6298 convnext_base_w-laion2b_s13b_b82k0.65280.6479 0.68140.7889 0.6262 convnext_base_w_320-laion_aesthetic_s13b_b82k0.67520.6647 0.68330.7833 0.6509 convnext_base_w_320-laion_aesthetic_s13b_b82k_augreg0.66940.6623 0.66290.7958 0.6505 convnext_large_d-laion2b_s26b_b102k_augreg0.71010.7092 0.70380.8098 0.6545 convnext_large_d_320-laion2b_s29b_b131k_ft0.69300.6866 0.68910.8059 0.6667 convnext_large_d_320-laion2b_s29b_b131k_ft_soup0.71060.7038 0.70060.8155 0.6695 convnext_xxlarge-laion2b_s34b_b82k_augreg0.74600.7446 0.77720.8653 0.7056 convnext_xxlarge-laion2b_s34b_b82k_augreg_soup0.74270.7435 0.77220.8636 0.7033 convnext_xxlarge-laion2b_s34b_b82k_augreg_rewind0.74520.7459 0.77550.8635 0.7036 ViT-B-16-datacomp_xl_s13b_b90k0.69120.6811 0.71710.7993 0.6481 ViT-B-32-datacomp_xl_s13b_b90k0.62580.6385 0.65630.7535 0.5838 ViT-L-14-datacomp_xl_s13b_b90k0.72170.7036 0.72540.7577 0.7326 ViT-L-14-laion400m_e320.64610.6460 0.65240.7590 0.6300 ViT-L-14-laion400m_e310.64520.6448 0.65250.7598 0.6297 ViT-L-14-laion2b_s32b_b82k0.64810.6535 0.65880.8017 0.6132 ViT-L-14-commonpool_xl_clip_s13b_b90k0.71460.7361 0.73290.8228 0.6497 ViT-L-14-commonpool_xl_laion_s13b_b90k0.74080.7493 0.75640.8109 0.6491 ViT-L-14-quickgelu-metaclip_400m0.70890.7473 0.76390.8186 0.6867 ViT-L-14-quickgelu-metaclip_fullcc0.75890.8029 0.80140.8394 0.6774 ViT-L-14-quickgelu-dfn2b0.70330.7388 0.73570.8239 0.6526 ViT-L-14-dfn2b_s39b0.67660.7611 0.76320.8353 0.6680 ViT-L-14-commonpool_xl_s13b_b90k0.72180.7670 0.78100.8336 0.6842 ViT-L-14-336-quickgelu-openai0.70460.7230 0.75980.8428 0.7269 ViT-H-14-quickgelu-metaclip_fullcc0.81720.8249 0.82770.8559 0.6668 ViT-H-14-quickgelu-dfn5b0.78200.8166 0.81450.8557 0.7048 ViT-H-14-worldwide-quickgelu-metaclip2_worldwide0.85990.9142 0.90820.9211 0.7557 ViT-H-14-378-quickgelu-dfn5b0.80950.8290 0.82820.8629 0.7339 ViT-H-14-worldwide-378-metaclip2_worldwide0.8892 0.9334 0.92990.9274 0.8053 ViT-bigG-14-quickgelu-metaclip_fullcc0.81070.8576 0.84690.8792 0.6965 ViT-bigG-14-worldwide-metaclip2_worldwide0.89210.9320 0.91640.9328 0.7968 ViT-bigG-14-worldwide-378-metaclip2_worldwide0.91690.9460 0.93530.9464 0.8399 34 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection Table 18|Pretraining objective affects transfer even without detector training. Mean ROC-Area Under CurveAUC (macro-averaged across the 24 mixed datasets in Percept-Lens evaluation datasets) for Gaussian discriminant heads conditioned on the sameCommunityForensicstraining prior (Park and Owens, 2025), using frozen encoders trained with different objectives. Frozen EncodersEuc-NCM (Wu et al., 2025b) Cos-NCMGNB Mah-NCMQDA CLIP-RoBERTa0.58120.58380.62080.72740.6025 CLIP-XLM-RoBERTa-Base0.59850.60870.63910.75860.5921 CLIP-XLM-RoBERTa-Large (Cherti et al., 2023)0.72640.72360.72610.84520.6492 MAE-Base0.52510.52270.53340.68730.5770 MAE-Large0.54340.54650.57690.70680.5672 MAE-Huge (He et al., 2022)0.54010.54020.58060.74180.5738 BEiT-Base0.51520.50600.51700.57150.5245 BEiT-Large (Bao et al., 2022)0.52030.51280.52080.60620.5363 SigLIP-Large (Zhai et al., 2023)0.52030.52940.52570.64740.5772 SigLIP-so400m0.52280.52130.52480.63450.5530 SigLIP2-Base-2240.52600.53370.52070.59980.5232 SigLIP2-Base-5120.52090.54820.51750.61230.5238 SigLIP2-Large-5120.54010.56840.53180.70560.5723 BLIP-Large (Li et al., 2022)0.54730.55110.53780.75350.5591 BLIP2 (Li et al., 2023)0.71870.71190.63590.83860.5871 coca_ViT-L-140.66540.66300.68590.80450.6089 coca_ViT-L-14-mscoco_finetuned0.56810.55540.58920.77580.5818 EVA01-g-14-laion400m_s11b_b41k0.72750.72180.69320.82750.5941 EVA01-g-14-plus-merged2b_s11b_b114k0.70630.76090.70520.84610.6488 EVA02-B-16-merged2b_s8b_b131k0.63050.62930.63370.76420.5929 EVA02-L-14-merged2b_s4b_b131k0.70020.72810.68870.79930.6163 CLIPA-ViT-L-140.69550.70490.71930.83040.6739 CLIPA-ViT-L-14-3360.71160.72230.73630.83500.6863 CLIPA-ViT-H-140.70730.73620.75000.86550.6997 CLIPA-ViT-bigG-14-3360.72060.78710.78490.88280.7302 nllb-clip-large-v10.72650.72370.72600.84520.6488 nllb-clip-large-siglip-v10.51870.50940.51090.69060.5632 nllb-clip-large-siglip-mrl0.48910.48270.50370.69680.5609 MobileCLIP2-L-140.71550.73130.76740.84150.6452 ViTamin-S0.60700.61170.64030.72380.6345 ViTamin-S-LTT0.62460.63790.62700.74250.6336 ViTamin-B0.65470.66010.66790.77130.6643 ViTamin-B-LTT0.64940.65420.65230.78480.6548 ViTamin-L0.68230.70580.73340.83580.7092 ViTamin-L-2560.69670.71800.73760.84350.7298 ViTamin-L-3360.70840.72660.74820.84730.7259 ViTamin-L-3840.74040.75940.79100.88140.6827 ViTamin-L20.71630.72070.74770.85000.7000 ViTamin-L2-2560.74180.74160.75480.85960.7268 ViTamin-L2-3360.74830.74390.76430.86710.7057 ViTamin-L2-3840.72440.72700.73590.82970.6634 ViTamin-XL-2560.76600.75890.78480.87700.7231 Continued on next page 35 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection Frozen EncodersEuc-NCM (Wu et al., 2025b) Cos-NCMGNB Mah-NCMQDA ViTamin-XL-3360.77740.77240.79360.87590.7089 ViTamin-XL-3840.77030.76430.78990.88160.7386 DINOv2-Small0.64550.65610.64190.68270.5546 DINOv2-Base0.67480.68350.66980.72750.5709 DINOv2-Large0.69290.69280.68950.75760.5813 DINOv2-Giant (Oquab et al., 2024)0.70070.71030.70210.80870.5896 DINOv3-ConvNeXt-Tiny0.59890.67000.59660.68720.5748 DINOv3-ConvNeXt-Small0.64800.67840.61030.70550.5865 DINOv3-ConvNeXt-Base0.68840.69320.65060.74060.6179 DINOv3-ConvNeXt-Large0.75190.72810.75540.80510.6768 DINOv3-ViT-S-160.65980.65460.65810.67880.5676 DINOv3-ViT-S-16+0.69170.68270.69470.69730.6048 DINOv3-ViT-B-160.76080.74030.76970.81050.6485 DINOv3-ViT-L-160.85390.80640.85930.88690.7490 DINOv3-ViT-H-16+0.89240.84470.87720.91110.8251 DINOv3-ViT-7B (Siméoni et al., 2025)0.91770.88360.89310.93420.8078 PE-Core-T-16-384-meta0.49600.49980.50570.63000.5215 PE-Core-S-16-384-meta0.60950.58500.62700.73140.6162 PE-Core-B-16-meta0.65270.64370.68790.80560.6356 PE-Core-L-14-336-meta0.87580.88060.90390.94250.8130 Tables 16 and 17 confirms that the encoder effect survives under a threshold-free metric. Within the OpenAI CLIP family, the best AUC improves from 0.7406 forResNet-50to 0.8345 forResNet-50x64, and from 0.7147 forViT-B/32to 0.8193 forViT-L/14. The broader OpenCLIP sweep spans a wider range, from 0.7076 to 0.9464, with several large H/bigG models above 0.92. As in CA, Mah-NCM is the modal winner, but the advantage is not universal. On some of the strongest encoders the gap to cosine or diagonal rules becomes negligible, and after correcting row-wise maxima there are isolated reversals. These reversals argue against presenting any one covariance assumption as universally correct. The head family still matters, but less than representation choice in this sweep. Table 18 shows a similarly large spread across encoder families, from 0.5715 forBeiT-Baseto 0.9425 forPE-Core-L-14-336-meta, withDINOv3-ViT-7balready reaching 0.9342. Several masked-image or SigLIP-style models remain well below the strongest contrastive or distilled models. This should still be written cautiously. The table does not isolate objective alone, because data scale, architecture, and resolution also change. What it does establish is that pretraining family is a first-order determinant of transfer even before any detector-specific optimization is introduced. In particular, language alignment is not a sufficient explanation: some language-aligned encoders are middling, whereas some visually distilled representations are exceptionally strong. 36 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection Table 20|Training prior dominates transfer even under a fixed encoder. Mean ROC-Area Under CurveAUC(macro- averaged across the 24 mixed datasets in Percept-Lens evaluation datasets) for Gaussian discriminant heads when varying only the support prior used to estimate moments, under the fixed frozenPE-Core-bigG-14-448encoder (Bolya et al., 2025). Training DatasetEuc-NCM (Wu et al., 2025b) Cos-NCM GNB Mah-NCM QDA CNNSpot (Wang et al., 2020)0.89870.9196 0.92100.9290 0.6466 GenImage (Zhu et al., 2023)0.8781 0.9624 0.94550.9589 0.9341 GenImage-SDv10.89740.9491 0.94670.9577 0.8407 DRCT-2M (Chen et al., 2024)0.85050.9260 0.91770.8716 0.9300 DRCT-SDv1 (Chen et al., 2024)0.8466 0.9508 0.93590.9372 0.9459 DRCT-SDv2 (Chen et al., 2024)0.8504 0.9551 0.94270.9551 0.9471 ELSA-D3 (Baraldi et al., 2025)0.91200.9363 0.94130.9645 0.9469 CommunityForensics (Park and Owens, 2025)0.89480.9309 0.94120.9693 0.9295 Table 19|QuickGELU versus GELU under a threshold-free metric. Mean ROC-Area Under CurveAUC(macro-averaged across the 24 mixed datasets in Percept-Lens evaluation datasets) for Gaussian discriminant heads conditioned on the same CommunityForensicstraining prior (Park and Owens, 2025), using frozen encoders that differ primarily in whether QuickGELU is used. Frozen EncoderEuc-NCM (Wu et al., 2025b) Cos-NCM GNB Mah-NCM QDA ViT-B-16-openai0.63100.6077 0.64980.7750 0.6500 ViT-B-16-quickgelu-openai0.63340.5965 0.65510.7823 0.6573 ViT-B-32-openai0.58190.5657 0.59280.6987 0.6027 ViT-B-32-quickgelu-openai0.60650.5831 0.61310.7147 0.6098 ViT-L-14-openai0.67080.6853 0.71340.8223 0.7012 ViT-L-14-quickgelu-openai0.66540.6911 0.71650.8193 0.7051 ViT-L-14-metaclip_400m0.69480.7266 0.74730.8088 0.6742 ViT-L-14-quickgelu-metaclip_400m0.70890.7473 0.76390.8186 0.6867 ViT-L-14-metaclip_fullcc0.73300.7898 0.78950.8347 0.6637 ViT-L-14-quickgelu-metaclip_fullcc0.75890.8029 0.80140.8394 0.6774 ViT-L-14-dfn2b0.71950.7480 0.74430.8188 0.6546 ViT-L-14-quickgelu-dfn2b0.70330.7388 0.73570.8239 0.6526 ViT-L-14-336-openai0.71150.7220 0.75370.8527 0.7253 ViT-L-14-336-quickgelu-openai0.70460.7230 0.75980.8428 0.7269 ViT-H-14-worldwide-metaclip20.85060.9081 0.90270.9108 0.7573 ViT-H-14-worldwide-quickgelu-metaclip20.85990.9142 0.90820.9211 0.7557 ViT-H-14-378-dfn5b0.79300.7988 0.80450.8558 0.7125 ViT-H-14-378-quickgelu-dfn5b0.80950.8290 0.82820.8629 0.7339 Table 19 suggests that the choice between GELU and QuickGELU is secondary relative to encoder family and scale. Most matched pairs differ by less than two AUC points, and the sign of the difference is not consistent across families. We therefore treat activation choice as a modest architecture-level modifier rather than a primary explanation for transfer. Table 20 shows that prior choice remains important even after fixing a strong encoder. The best AUC varies from 0.9290 withCNNSpotsupport to 0.9693 withCommunityForensicssupport. More importantly, the preferred Gaussian rule depends on the prior:CommunityForensicsandELSA-D3 favor Mah-NCM,DRCT-2Mfavors QDA or cosine, andGenImagefavors cosine once the row-wise maximum is corrected. Thus, the covariance structure that transfers best is prior-conditioned rather than universal. At the per-dataset level, the AUC table (Table 21) shows both the breadth and the limits of the 37 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection Table 21|Per-dataset AUC under a fixed encoder and varying training prior. ROC-Area Under CurveAUCfor individual datasets in Percept-Lens evaluation mixed datasets (24 datasets total) for Gaussian discriminant heads, under the fixed frozenPE-Core-bigG-14-448encoder (Bolya et al., 2025) and the fixedCommunityForensicssupport prior (Park and Owens, 2025). Training DatasetEuc-NCM (Wu et al., 2025b) Cos-NCM GNB Mah-NCM QDA FourierSpectrumDiscrepancies (Dzanic et al., 2020)0.85690.8996 0.95511.0000 0.9956 FakeInversion (Cazenavette et al., 2024)0.87140.9811 0.95880.9997 0.9844 UniversalFakeDetect (Ojha et al., 2023)0.99000.9982 0.99800.9998 0.9906 Dalle Recognition Dataset (Koliha, 2024)0.90870.9457 0.95280.9916 0.9708 Chameleon (Yan et al., 2024)0.95480.9549 0.96740.9932 0.8537 AIGI-Detection-Quality-Paradox (Xiao et al., 2025)0.87140.9668 0.97680.9992 0.9909 DiTFake (Li et al., 2025b)0.95040.9989 0.99790.9995 0.9935 Diffusion1kSteps (Tan et al., 2024)0.90250.9127 0.95860.9873 0.9234 GANGen-Detection (Chuangchuang Tan, 2024)0.98910.9890 0.99390.9979 0.9876 RobustLDM (Rajan et al., 2024)0.93780.9549 0.96590.9973 0.9397 RealRobustBench (Li et al., 2025a)0.84450.8670 0.88200.9923 0.8071 LDMFakeDetect (Rajan and Lee, 2025)0.93420.9509 0.96410.9959 0.9335 DIF (Sinitsa and Fried, 2024)0.91840.9884 0.99180.9995 0.9904 ForenSynths (Wang et al., 2020)0.78580.9413 0.93830.9947 0.9748 DNF-TestSet (Zhang and Xu, 2025)0.99490.9978 0.99900.9999 0.9949 DeepFakeFace (Song et al., 2023)0.85000.8490 0.84240.9346 0.8261 AIGCDetectBench (Zhong et al., 2024)0.94630.9884 0.98970.9975 0.9806 AIGI-Holmes (Zhou et al., 2025b)0.93480.9744 0.98920.9988 0.9860 AI-Artwork (Kholy, 2024)0.91630.9383 0.96700.9913 0.9714 DiffusionForensics (Wang et al., 2023)0.9701 0.9916 0.99050.9912 0.9505 B-Free (Guillaro et al., 2025)0.91400.9373 0.93620.9439 0.9294 LASTED (Wu et al., 2025a)0.77660.8022 0.82500.8008 0.7916 AIGIBench (Li et al., 2025c)0.89410.9539 0.98170.9843 0.9545 DeepFakeBench (Yan et al., 2023)0.56200.5595 0.56660.6735 0.5865 Table 22|Data-efficiency of moment-based heads. Mean ROC-Area Under CurveAUC(macro-averaged across the 24 mixed datasets in Percept-Lens evaluation datasets) for Gaussian discriminant heads as the support set used to estimate moments is subsampled fromCommunityForensics(Park and Owens, 2025), under the fixed frozenPE-Core-bigG-14-448 encoder (Bolya et al., 2025). (Superscript/subscript denote max/min deviations (in percentage points) from the reported mean). Amount Euc-NCM (Wu et al., 2025b) Cos-NCMGNBMah-NCMQDA 0.001%0.8345 +0.0224 −0.0407 0.9356 +0.0037 −0.0042 0.9239 +0.0134 −0.0185 0.8788 +0.0132 −0.0187 0.9025 +0.0277 −0.0148 0.005%0.8852 +0.0052 −0.0032 0.9313 +0.0041 −0.0036 0.9379 +0.0039 −0.0032 0.9383 +0.0037 −0.0049 0.9089 +0.0122 −0.0137 0.01%0.8897 +0.0080 −0.0044 0.9319 +0.0018 −0.0029 0.9396 +0.0052 −0.0048 0.9469 +0.0061 −0.0045 0.8991 +0.0166 −0.0197 0.1%0.8919 +0.0050 −0.0036 0.9303 +0.0036 −0.0032 0.9403 +0.0015 −0.0013 0.9638 +0.0017 −0.0019 0.8308 +0.0044 −0.0119 1%0.8947 +0.0010 −0.0012 0.9310 +0.0009 −0.0010 0.9410 +0.0002 −0.0001 0.9668 +0.0014 −0.0008 0.8478 +0.0035 −0.0054 100%0.89480.93090.94120.96930.9295 average improvement. Mah-NCM reaches near-ceiling AUC on many mixed benchmarks, including RealRobustBench(Li et al., 2025a) (0.9923),ForenSynths(Wang et al., 2020) (0.9947), and AIGI-Holmes(Zhou et al., 2025b) (0.9988), so the macro-average is not driven by a small subset of low-difficulty benchmarks. The failure cases are also informative.LASTEDfavors GNB, DiffusionForensics(Wang et al., 2023) is effectively tied between cosine and Mahalanobis, and DeepFakeBench(Yan et al., 2023) remains difficult for every head, peaking at only 0.6735. Comparing Table 21 with Table 14 is especially informative onDiffusionForensics: Mah-NCM is not best in CA but is essentially tied for best in AUC, suggesting that the representation contains ranking signal even though the default operating point is suboptimal. 38 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection Table 22 adds a small-data qualifier. At the smallest support size, simpler rules can be more reliable than shared full-covariance estimation. With only 0.001% ofCommunityForensics, Cos-NCM already reaches 0.9356 AUC, whereas Mah-NCM drops to 0.8788. Mah-NCM overtakes once modest support is available, reaching 0.9638 at 0.1% and 0.9668 at 1%, close to the full-support 0.9693. QDA is visibly unstable and non-monotone under subsampling, consistent with a higher-variance class-specific covariance estimate. For few-shot adaptation, the data do not support the general rule “always use the richest Gaussian model.” They support the more specific rule “match the covariance model to the amount of support available.” Overall, the AUC results do not merely replicate the CA results. The threshold-free view strengthens the main claim. Low-order feature geometry remains highly competitive, while the failure cases show that the residual value of a trained head, when it exists, is real but narrower than many standalone detector comparisons suggest. G. Class-Conditional Gaussianity Diagnostics of Evaluation Features A natural objection to the Gaussian ladder is that frozen-encoder features on shifted evaluation data need not be exactly Gaussian. The relevant object, however, is the class-conditional feature distribution 푝 휙 (푧 | 푦= 푐,D), not the pooled distribution푝 휙 (푧 | D): even if each class-conditional component were Gaussian, their mixture would in general not be Gaussian. We therefore report class-conditional Gaussianity diagnostics for each dataset–class subset in feature space. These quantities are diagnostics, not formal hypothesis tests. They summarize departures from Gaussian structure, but they do not provide calibrated푝-values and should not be interpreted as accepting or rejecting exact normality. Let푧 푖 = 휙(푥 푖 ) ∈ ℝ 푑 denote the frozen-encoder feature of sample푥 푖 , restricted to a fixed dataset Dand class푐 ∈ 0,1. With푛samples in that subset, empirical mean ̄푧, and regularized sample covariance b Σ= 1 푛− 1 푛 ∑︁ 푖=1 (푧 푖 − ̄푧)(푧 푖 − ̄푧) ⊤ + 휀퐼 푑 , 휀= 10 −8 ,(G.1) we compute both marginal and multivariate diagnostics. Finite-sample caveats. Marginal skewness/kurtosis estimates can be noisy when the subset size푛 is small, and multivariate diagnostics based on Mahalanobis radii require푛 > 푑for a well-conditioned full-rank covariance estimate. Accordingly, we interpret large deviations most strongly on dataset– class subsets with ample sample sizes, and we treat results for very small subsets as qualitative indicators rather than definitive evidence of non-Gaussianity. For each coordinate푗 ∈ 1, . . . , 푑, letˆ훾 1,푗 andˆ훾 2,푗 denote the bias-corrected sample skewness and Pearson kurtosis, respectively, so that the Gaussian reference isˆ훾 1,푗 =0 andˆ훾 2,푗 =3. We summarize these marginal statistics by their median and interquartile range across dimensions, and we report the proportion of dimensions satisfying the loose Gaussian screen PctClose= 100 푑 푑 ∑︁ 푗=1 1 |ˆ훾 1,푗 | < 0.5 ∧ 2 < ˆ훾 2,푗 < 5 .(G.2) At the multivariate level, we compute the empirical squared Mahalanobis radii 훿 2 푖 =(푧 푖 − ̄푧) ⊤ b Σ −1 (푧 푖 − ̄푧),(G.3) 39 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection and the normalized Mardia kurtosis e 훽 2,푑 = 1 푑(푑+ 2) · 1 푛 푛 ∑︁ 푖=1 (훿 2 푖 ) 2 ,(G.4) whose Gaussian reference value is 1. For completeness, we also report 푅 휒 2 = 1 푛푑 푛 ∑︁ 푖=1 훿 2 푖 .(G.5) 푅 휒 2 should be interpreted with caution because b Σis estimated from the same sample, and therefore 1 푛푑 푛 ∑︁ 푖=1 훿 2 푖 ≈ 푛− 1 푛 (G.6) in the ideal full-rank unregularized setting, so values near 1 are largely expected and do not constitute strong evidence of Gaussianity. To summarize the second-order geometry of each class-conditional feature cloud, let휆 1 ≥ · ≥ 휆 푑 denote the eigenvalues of b Σ and define 푝 푗 = 휆 푗 / Í 푑 푘=1 휆 푘 . We report the effective rank 퐸 rank ( b Σ)= exp © « − 푑 ∑︁ 푗=1 푝 푗 log 푝 푗 ª ® ¬ ,(G.7) which can be interpreted as the effective number of principal directions carrying variance, and the anisotropy Aniso( b Σ)= 휆 1 1 푑 Í 푑 푗=1 휆 푗 = 푑 휆 1 tr( b Σ) ,(G.8) which equals 1 for isotropic covariance and increases as variance concentrates into a small number of directions. Table 23|Marginal Gaussianity diagnostics for class-conditional evaluation features. For each dataset–class subset, we compute the bias-corrected sample skewnessˆ훾 1,푗 and Pearson kurtosisˆ훾 2,푗 for every feature dimension푗. We report the median with first/third quartiles [Q1,Q3] across dimensions, together with the percentage of dimensions satisfying the heuristic Gaussian screen|ˆ훾 1,푗 | <0.5 and 2< ˆ훾 2,푗 <5. These quantities are descriptive diagnostics rather than formal normality tests. DatasetClassˆ훾 1,푗 ˆ훾 2,푗 PctClose Out-of-Distribution Existing Datasets with only Real Images Unsplash (uns)Real0.0045 [-0.07,0.08]3.0577 [2.99,3.13]99.77 InstagramImagesWithCaptions (ins)Real-0.0001 [-0.07,0.06]3.0327 [2.97,3.01]98.98 AnimeFace (Churchill and Chao, 2019)Real-0.0058 [-0.16,0.16]3.1563 [3.01,3.30]94.45 AnimeImages (Banana_Leopard, 2023)Real-0.0027 [-0.08,0.08]3.0867 [3.02,3.17]99.53 CelebA-Spoof (Zhang et al., 2020)Real-0.0081 [-0.12,0.12]3.1013 [2.99,3.21]99.38 Out-of-Distribution Existing Datasets with only Synthetic Images AGIQA-1k (Zhang et al., 2023)Fake-0.0034 [-0.13,0.11]2.9904 [2.84,3.16]97.81 AGIQA-3k (Li et al., 2024)Fake-0.0037 [-0.09,0.09]3.0732 [2.97,3.19]99.45 SPAI (Karageorgiou et al., 2025)Fake0.0018 [-0.06,0.06]3.0477 [2.97,3.14]99.69 Continued on next page 40 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection DatasetClassˆ훾 1,푗 ˆ훾 2,푗 PctClose SynthBuster Extended (Bammey, 2024; Guillaro et al., 2025) Fake-0.0004 [-0.08,0.07]3.0470 [2.96,3.14]99.38 SynthScars (Kang et al., 2025)Fake-0.0037 [-0.06,0.05]3.0438 [2.98,3.11]99.92 GigaGAN (Kang et al., 2023)Fake0.0016 [-0.08,0.08]3.1237 [3.05,3.12]100.00 LatentDiffusion (Corvi et al., 2023)Fake0.0043 [-0.08,0.09]3.0735 [2.95,3.19]99.45 MidjourneyV6 (ter)Fake0.0008 [-0.04,0.04]3.0391 [2.99,3.09]100.00 Co-Spy-Bench (Cheng et al., 2025)Fake-0.0005 [-0.05,0.05]3.0572 [3.01,3.11]100.00 Dalle3 (Egan et al., 2024)Fake0.0003 [-0.04,0.04]3.0211 [2.98,3.06]99.38 Out-of-Distribution Existing Datasets with both Real and Synthetic Images FourierSpectrumDiscrepancies (Dzanic et al., 2020) Real-0.0496 [-0.41,0.35]2.4977 [2.01,3.16]38.44 FourierSpectrumDiscrepancies (Dzanic et al., 2020) Fake0.0286 [-0.31,0.33]2.9860 [2.60,3.52]70.39 FakeInversion (Cazenavette et al., 2024)Real0.0027 [-0.08,0.09]3.0182 [2.88,3.18]99.69 FakeInversion (Cazenavette et al., 2024)Fake-0.0019 [-0.08,0.09]3.0231 [2.89,3.18]100.0 UniversalFakeDetect (Ojha et al., 2023) Real0.0019 [-0.06,0.06]3.0278 [2.94,3.12]99.22 UniversalFakeDetect (Ojha et al., 2023) Fake0.0021 [-0.07,0.07]3.1456 [3.07,3.25]99.84 DalleRecognition (Koliha, 2024)Real0.0025 [-0.07,0.08]3.0176 [2.92,3.12]99.61 DalleRecognition (Koliha, 2024)Fake-0.0002 [-0.04,0.05]3.0393 [2.98,3.10]99.77 Chameleon (Yan et al., 2024)Real0.0000 [-0.05,0.05]3.0130 [2.96,3.07]100.0 Chameleon (Yan et al., 2024)Fake-0.0073 [-0.09,0.08]3.0824 [2.99,3.19]99.84 AIGI-Detection-Quality-Paradox (Xiao et al., 2025) Real-0.0002 [-0.05,0.05]3.0274 [2.96,3.12]98.36 AIGI-Detection-Quality-Paradox (Xiao et al., 2025) Fake-0.0020 [-0.07,0.07]3.0670 [2.99,3.15]99.84 DiTFake (Li et al., 2025b)Real0.0054 [-0.05,0.06]3.0002 [2.93,3.07]99.84 DiTFake (Li et al., 2025b)Fake0.0043 [-0.07,0.08]2.9940 [2.91,3.09]100.0 Diffusion1kStep (Tan et al., 2024)Real0.0062 [-0.07,0.08]3.0114 [2.92,3.11]98.67 Diffusion1kStep (Tan et al., 2024)Fake-0.0010 [-0.16,0.17]3.1901 [2.99,3.39]97.27 GANGen-Detection (Chuangchuang Tan, 2024) Real-0.0022 [-0.10,0.11]3.1389 [3.02,3.28]97.27 GANGen-Detection (Chuangchuang Tan, 2024) Fake0.0091 [-0.17,0.19]3.3372 [3.19,3.51]94.38 RobustLDM (Rajan et al., 2024)Real0.0029 [-0.07,0.07]3.0167 [2.93,3.11]99.77 RobustLDM (Rajan et al., 2024)Fake-0.0015 [-0.10,0.10]3.0445 [2.93,3.17]99.38 RealRobustBench (Li et al., 2025a)Real0.0017 [-0.06,0.07]3.0111 [2.94,3.08]99.69 RealRobustBench (Li et al., 2025a)Fake0.0038 [-0.09,0.10]3.0029 [2.90,3.13]99.22 LDMFakeDetect (Rajan and Lee, 2025)Real0.0029 [-0.07,0.07]3.0167 [2.93,3.11]99.77 LDMFakeDetect (Rajan and Lee, 2025)Fake-0.0044 [-0.10,0.09]3.0534 [2.95,3.19]99.45 DIF (Sinitsa and Fried, 2024)Real0.0001 [-0.06,0.06]3.0288 [2.97,3.09]99.84 DIF (Sinitsa and Fried, 2024)Fake0.0032 [-0.09,0.10]3.0732 [2.94,3.21]99.53 ForenSynths (Wang et al., 2020)Real0.0143 [-0.23,0.24]3.2898 [2.97,3.50]97.27 ForenSynths (Wang et al., 2020)Fake0.0119 [-0.20,0.23]3.1450 [2.84,3.40]93.98 DNFTestSet (Zhang and Xu, 2025)Real0.0006 [-0.06,0.07]3.0247 [2.95,3.10]99.69 DNFTestSet (Zhang and Xu, 2025)Fake0.0038 [-0.11,0.13]3.1119 [2.95,3.24]99.45 DeepFakeFace (Song et al., 2023)Real-0.0021 [-0.06,0.06]3.0008 [2.95,3.06]99.84 DeepFakeFace (Song et al., 2023)Fake-0.0027 [-0.09,0.08]3.0757 [3.01,3.15]99.84 AIGCDetectBench (Zhong et al., 2024)Real0.0020 [-0.05,0.05]3.0221 [2.97,3.07]99.61 AIGCDetectBench (Zhong et al., 2024)Fake0.0079 [-0.09,0.10]3.1043 [3.00,3.21]99.61 Continued on next page 41 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection DatasetClassˆ훾 1,푗 ˆ훾 2,푗 PctClose AIGI-Holmes (Zhou et al., 2025b)Real0.0012 [-0.05,0.05]3.0068 [2.95,3.06]99.77 AIGI-Holmes (Zhou et al., 2025b)Fake0.0000 [-0.09,0.09]3.0812 [2.99,3.17]100.0 AI-Artwork (Kholy, 2024)Real-0.0032 [-0.06,0.06]3.0122 [2.95,3.08]99.77 AI-Artwork (Kholy, 2024)Fake0.0050 [-0.12,0.12]3.0849 [2.95,3.23]99.30 DiffusionForensics (Wang et al., 2023)Real0.0079 [-0.12,0.12]3.1291 [3.02,3.22]99.45 DiffusionForensics (Wang et al., 2023)Fake0.0071 [-0.31,0.32]3.7335 [3.49,4.01]71.48 B-Free (Guillaro et al., 2025)Real0.0049 [-0.05,0.06]2.9950 [2.93,3.07]99.92 B-Free (Guillaro et al., 2025)Fake0.0006 [-0.06,0.06]3.0396 [2.98,3.10]100.0 LASTED (Wu et al., 2025a)Real0.0078 [-0.06,0.07]3.0478 [2.98,3.11]100.0 LASTED (Wu et al., 2025a)Fake-0.0028 [-0.12,0.12]3.2195 [3.11,3.34]99.22 AIGIBench (Li et al., 2025c)Real0.0001 [-0.06,0.06]3.0447 [2.99,3.11]99.92 AIGIBench (Li et al., 2025c)Fake0.0067 [-0.11,0.13]3.1626 [3.05,3.28]99.77 DeepFakeBench (Yan et al., 2023)Real-0.0008 [-0.17,0.18]3.1662 [2.97,3.34]98.52 DeepFakeBench (Yan et al., 2023)Fake0.0101 [-0.16,0.17]3.0508 [2.75,3.31]94.69 Table 24|Multivariate diagnostics for class-conditional evaluation features. Let푟 푖 = 푧 푖 − ̄푧and let b Σbe the regularized sample covariance of the class-conditional features. We compute squared Mahalanobis radii훿 2 푖 = 푟 ⊤ 푖 b Σ −1 푟 푖 . We report (i) the normalized Mardia kurtosis e 훽 2,푑 = 1 푑(푑+2) 1 푛 Í 푛 푖=1 (훿 2 푖 ) 2 , whose Gaussian reference value is 1, (i) the normalized mean radius푅 휒 2 = 1 푛푑 Í 푛 푖=1 훿 2 푖 (a limited self-consistency diagnostic; with same-sample mean/covariance estimation it is expected to be near 1 even under non-Gaussianity), and two spectrum/conditioning summaries of b Σ: (i) the effective rank퐸 rank = exp − Í 푑 푗=1 푝 푗 log 푝 푗 with푝 푗 = 휆 푗 / Í 푘 휆 푘 , and (iv) anisotropyAniso= 휆 1 / 1 푑 Í 푑 푗=1 휆 푗 = 푑휆 1 /tr( b Σ) , where 휆 1 ≥ · ≥ 휆 푑 are the eigenvalues of b Σ.퐸 rank ∈ [1, 푑]summarizes effective dimensionality, whileAniso ≥1 measures dominance of the top variance direction. All quantities are descriptive diagnostics rather than calibrated hypothesis tests. (Note: We report dataset/classes where number of samples is greater than number of feature dimensions.) DatasetClass e 훽 2,푑 푅 휒 2 퐸 rank Aniso Out-of-Distribution Existing Datasets with only Real Images Unsplash (uns)Real 1.1225 0.9998 227.80 75.23 InstagramImagesWithCaptions (ins)Real 1.1092 0.9998 251.47 74.98 AnimeFace (Churchill and Chao, 2019)Real 1.1957 0.9995 61.89 293.73 AnimeImages (Banana_Leopard, 2023)Real 1.1715 0.9998 254.45 61.78 CelebA-Spoof (Zhang et al., 2020)Real 1.1694 0.9998 171.74 166.86 Out-of-Distribution Existing Datasets with only Synthetic Images AGIQA-3k (Li et al., 2024)Fake 1.0319 0.9992 210.56 76.71 SPAI (Karageorgiou et al., 2025)Fake 1.0574 0.9994 267.96 51.12 SynthBuster Extended (Bammey, 2024; Guillaro et al., 2025) Fake 1.0879 0.9996 194.50 91.25 SynthScars (Kang et al., 2025)Fake 1.0690 0.9997 250.11 60.05 GigaGAN (Kang et al., 2023)Fake 1.1644 0.9998 268.03 80.58 LatentDiffusion (Corvi et al., 2023)Fake 1.1179 0.9997 212.48 76.55 MidjourneyV6 (ter)Fake 1.0934 0.9998 281.47 50.06 Co-Spy-Bench (Cheng et al., 2025)Fake 1.0772 0.9998 299.09 39.92 Dalle3 (Egan et al., 2024)Fake 1.0995 0.9998 280.66 54.19 Continued on next page 42 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection DatasetClass e 훽 2,푑 푅 휒 2 퐸 rank Aniso Out-of-Distribution Existing Datasets with both Real and Synthetic Images UniversalFakeDetect (Ojha et al., 2023)Real 1.0030 0.9991 339.72 76.99 UniversalFakeDetect (Ojha et al., 2023)Fake 1.0742 0.9996 282.82 52.51 DalleRecognition (Koliha, 2024)Real 1.0335 0.9995 229.58 111.29 DalleRecognition (Koliha, 2024)Fake 1.0719 0.9997 291.76 39.74 Chameleon (Yan et al., 2024)Real 1.0619 0.9997 262.78 77.87 Chameleon (Yan et al., 2024)Fake 1.1232 0.9996 194.40 119.96 AIGI-Detection-Quality-Paradox (Xiao et al., 2025)Real 1.0430 0.9995 319.79 61.35 AIGI-Detection-Quality-Paradox (Xiao et al., 2025)Fake 1.1087 0.9997 263.10 55.39 DiTFake (Li et al., 2025b)Real 1.0507 0.9997 281.90 51.76 DiTFake (Li et al., 2025b)Fake 1.0900 0.9997 213.86 58.78 Diffusion1kStep (Tan et al., 2024)Real 1.0448 0.9997 222.71 109.72 Diffusion1kStep (Tan et al., 2024)Fake 1.2005 0.9997 148.31 148.77 GANGen-Detection (Chuangchuang Tan, 2024)Real 1.1642 0.9997 187.29 101.55 GANGen-Detection (Chuangchuang Tan, 2024)Fake 1.2674 0.9996 146.67 122.43 RobustLDM (Rajan et al., 2024)Real 1.0408 0.9996 249.19 98.38 RobustLDM (Rajan et al., 2024)Fake 1.2930 0.9997 177.50 72.18 RealRobustBench (Li et al., 2025a)Real 1.0891 0.9998 239.64 73.09 RealRobustBench (Li et al., 2025a)Fake 1.1513 0.9997 173.27 98.95 LDMFakeDetect (Rajan and Lee, 2025)Real 1.0408 0.9996 249.19 98.38 LDMFakeDetect (Rajan and Lee, 2025)Fake 1.3017 0.9997 178.20 71.55 DIF (Sinitsa and Fried, 2024)Real 1.0587 0.9998 309.16 60.52 DIF (Sinitsa and Fried, 2024)Fake 1.1797 0.9997 192.48 89.98 ForenSynths (Wang et al., 2020)Real 1.2396 0.9998 182.97 193.47 ForenSynths (Wang et al., 2020)Fake 1.2685 0.9997 104.62 218.03 DNFTestSet (Zhang and Xu, 2025)Real 1.0450 0.9997 274.26 84.16 DNFTestSet (Zhang and Xu, 2025)Fake 1.1293 0.9997 198.64 117.17 DeepFakeFace (Song et al., 2023)Real 1.0758 0.9998 237.47 74.91 DeepFakeFace (Song et al., 2023)Fake 1.1205 0.9998 221.72 72.87 AIGCDetectBench (Zhong et al., 2024)Real 1.0540 0.9998 323.16 69.08 AIGCDetectBench (Zhong et al., 2024)Fake 1.1375 0.9997 228.13 83.67 AIGI-Holmes (Zhou et al., 2025b)Real 1.0686 0.9998 303.84 49.64 AIGI-Holmes (Zhou et al., 2025b)Fake 1.1375 0.9998 222.87 64.21 AI-Artwork (Kholy, 2024)Real 1.0767 0.9998 220.19 71.57 AI-Artwork (Kholy, 2024)Fake 1.2529 0.9997 144.42 114.62 DiffusionForensics (Wang et al., 2023)Real 1.1251 0.9998 236.08 129.66 DiffusionForensics (Wang et al., 2023)Fake 1.4326 0.9997 144.56 190.06 B-Free (Guillaro et al., 2025)Real 1.0637 0.9998 278.64 52.92 Continued on next page 43 Prior-Conditioned Gaussian Discriminants for Generalizable AI-generated Image Detection DatasetClass e 훽 2,푑 푅 휒 2 퐸 rank Aniso B-Free (Guillaro et al., 2025)Fake 1.0798 0.9998 267.28 55.60 LASTED (Wu et al., 2025a)Real 1.0803 0.9998 300.73 58.42 LASTED (Wu et al., 2025a)Fake 1.3136 0.9997 210.48 111.79 AIGIBench (Li et al., 2025c)Real 1.0864 0.9998 303.42 65.94 AIGIBench (Li et al., 2025c)Fake 1.1784 0.9998 217.27 77.97 DeepFakeBench (Yan et al., 2023)Real 1.1376 0.9996 128.46 208.58 DeepFakeBench (Yan et al., 2023)Fake 1.2176 0.9996 73.41 310.36 Applied to features from the strongest frozen encoder in our sweep,PE-Core-bigG-14-448(Bolya et al., 2025), the diagnostics support Gaussian heads as approximate second-order models, but not as exact density models. In Table 23, most dataset–class subsets have median skewness near zero, median Pearson kurtosis near three, and highPctClose, often above 97%. The clearest marginal exceptions are the real and fake subsets ofFourierSpectrumDiscrepancies(Dzanic et al., 2020) and the fake subset ofDiffusionForensics(Wang et al., 2023), where deviations from the Gaussian reference are large. For the Gaussian ladder, the multivariate diagnostics in Table 24 are more relevant. The normalized Mardia kurtosis e 훽 2,푑 is often only moderately above its Gaussian reference value of 1, but the larger deviations occur disproportionately in fake subsets. These same subsets frequently exhibit lower effective rank and higher anisotropy than their real counterparts, indicating that variance is concentrated in fewer dominant directions. This pattern is not universal, but it recurs often enough to make covariance-aware scoring plausible. By contrast,푅 휒 2 remains close to 1 almost everywhere, as expected under same-sample estimation, and should be interpreted only as a consistency check. The resulting conclusion is deliberately narrow. Evaluation features are not exactly Gaussian, and several datasets exhibit clear departures from Gaussianity. For many dataset–class subsets, however, first- and second-order summaries describe a useful part of the class structure, while the failures mark cases where higher-order or multimodal structure likely matters. This supports Gaussian heads as controlled, interpretable probes in matched support-prior and encoder audits, not as literal generative models of the feature distribution. Read together with the transfer results, these diagnostics support a methodological claim rather than a distributional one: when the support prior and frozen encoder feature space are fixed, Gaussian heads indicate the extent to which the observed head-level behavior is already available in low-order geometry. They do not imply that low-order geometry is the only transfer mechanism or that Gaussian assumptions hold globally. Head-level comparisons are therefore most interpretable when both quantities are controlled. 44