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What Makes a Good Medical Image Tokenizer? Rethinking Reconstruction and Generation in Medical Image Tokenization
Niklas Bubeck, Yundi Zhang, Vasiliki Sideri-Lampretsa, Julian McGinnis, Jiancheng Yang, Daniel Rueckert, Jiazhen Pan
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Abstract
Abstract:Latent diffusion models now dominate medical image generation, and every such pipeline rests on a \emph{tokenizer} that compresses images into the latent codes for image generation to operate on. Thereby, the tokenizer choice bounds every downstream task from reconstruction fidelity and generation quality to the representations available for downstream analysis. Yet, medical imaging pipelines routinely utilize tokenizers from natural imaging on the hypothesis that their behavior carries over. However, this is an assumption never tested in the medical imaging regime, where datasets are orders of magnitude smaller and images exhibit far lower inter-sample variance. We present a systematic evaluation of medical image tokenizers evaluating thirty configurations across ten model families on twelve datasets at three compression factors, spanning reconstruction, generation, latent geometry, downstream classification, and memorization. We find that (1) performance on image reconstruction and generation strongly correlate, unlike prior reports on natural images; (2) modern tokenizers use nearly all of their codebook entries, but still leave most of the latent space unused; (3) training-set memorization is mild and is further suppressed by stronger latent space compression; and (4) discrete quantization can largely preserve downstream classification, with lookup-free schemes being the main exception.
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- Source: https://arxiv.org/abs/2609.24691v1
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What Makes a Good Medical Image Tokenizer? Rethinking Reconstruction and Generation in Medical Image Tokenization Niklas Bubeck Affiliation: School of Computation, Information and Technology, Technical University of Munich, Germany Affiliation: Munich Center for Machine Learning, Technical University of Munich, Germany Affiliation: School of Medicine, Klinikum rechts der Isar, Technical University of Munich, Germany Email: niklas.bubeck@tum.de Yundi Zhang Affiliation: School of Computation, Information and Technology, Technical University of Munich, Germany Affiliation: School of Medicine, Klinikum rechts der Isar, Technical University of Munich, Germany Vasiliki Sideri-Lampretsa Affiliation: School of Computation, Information and Technology, Technical University of Munich, Germany Affiliation: School of Medicine, Klinikum rechts der Isar, Technical University of Munich, Germany Julian McGinnis Affiliation: School of Computation, Information and Technology, Technical University of Munich, Germany Affiliation: School of Medicine, Klinikum rechts der Isar, Technical University of Munich, Germany Jiancheng Yang Affiliation: ELLIS Institute Finland, Finland School of Electrical Engineering, Aalto University, Finland Daniel Rueckert Affiliation: School of Computation, Information and Technology, Technical University of Munich, Germany Affiliation: Munich Center for Machine Learning, Technical University of Munich, Germany Affiliation: School of Medicine, Klinikum rechts der Isar, Technical University of Munich, Germany Affiliation: Department of Computing, Imperial College London, UK Jiazhen Pan Affiliation: School of Computation, Information and Technology, Technical University of Munich, Germany Affiliation: Munich Center for Machine Learning, Technical University of Munich, Germany Affiliation: School of Medicine, Klinikum rechts der Isar, Technical University of Munich, Germany Abstract Latent diffusion models now dominate medical image generation, and every such pipeline rests on a tokenizer that compresses images into the latent codes for image generation to operate on. Thereby, the tokenizer choice bounds every downstream task from reconstruction fidelity and generation quality to the representations available for downstream analysis. Yet, medical imaging pipelines routinely utilize tokenizers from natural imaging on the hypothesis that their behavior carries over. However, this is an assumption never tested in the medical imaging regime, where datasets are orders of magnitude smaller and images exhibit far lower inter-sample variance. We present a systematic evaluation of medical image tokenizers evaluating thirty configurations across ten model families on twelve datasets at three compression factors, spanning reconstruction, generation, latent geometry, downstream classification, and memorization. We find that (1) performance on image reconstruction and generation strongly correlate, unlike prior reports on natural images; (2) modern tokenizers use nearly all of their codebook entries, but still leave most of the latent space unused; (3) training-set memorization is mild and is further suppressed by stronger latent space compression; and (4) discrete quantization can largely preserve downstream classification, with lookup-free schemes being the main exception.† To foster research in this direction, we will open-source the framework and all models upon acceptance. 1 Introduction Figure 1: Method Overview. We take quantizers out of the library and evaluate them on diverse medical imaging datasets to study whether prevalent assumptions from natural imaging transfer to the medical domain. Medical imaging faces persistent challenges: limited data hinders generalization [1], expert annotations are costly [2], and strict privacy regulations constrain data sharing [3, 4]. Generative AI offers a compelling path forward, enabling synthetic augmentation, report-to-image synthesis, and latent compression for efficient analysis. Generative models have become dominant across a wide range of medical imaging applications [5, 6], including MRI reconstruction [7, 8], 3D CT and MRI generation [4, 9, 10], chest X-ray synthesis from radiology reports [11, 12], controllable lesion editing [13], pathology and dermatology synthesis [14, 15, 16, 17], retinal imaging [18, 19, 20], and cell morphology modeling [21, 22]. Across all of these fields, generation is built almost exclusively on diffusion over a continuous latent, while autoregressive and discrete-token models remain comparatively rare and task-specific [23, 24, 25, 26]. That latent is produced by a tokenizer, which compresses high-dimensional images into the compact space on which the generator operates. Its choice bounds everything from downstream task performance to generation quality, yet most medical pipelines adopt off-the-shelf quantizers without systematic justification, transferring conclusions from natural imaging. In this paper, we study tokenizers as substrates for latent diffusion, which underpins most medical generative pipelines, and challenge the prevailing approach, which carries over assumptions from natural images, and question this transfer, which remains understudied. The first is that reconstruction quality is a poor proxy for generation quality, with recent work instead attributing generation performance to global semantic information and spatial structure in the latent space [27, 28, 29, 30]. The second is that a healthy codebook, having high utilization and no collapse, signals an expressive latent space [31, 32, 33, 34] leading to improved generation performance. Both were established on ImageNet-scale natural images, but medical data occupy a fundamentally different statistical regime: collections are small and highly repetitive, images of the same organ share a global layout and differ only in subtle, localized detail, and the diagnostically meaningful signal often lives in fine-grained, high-frequency texture [35], such as a faint lesion, that a tokenizer must preserve exactly. With less data to learn from, lower variation between samples, and a narrower margin for error, conclusions drawn from natural images may not transfer cleanly to medical imaging. In consequence, we challenge the current practice and call for a careful re-examination before they are relied upon in this domain. Medical imaging raises two additional concerns that natural image tokenizers were never designed to address. First, synthetic medical data is valuable mainly because it protects patient privacy, but that benefit disappears if the model memorizes and reproduces real patients [3, 36]. Whether the tokenizer’s compression bottleneck affects this leakage has not yet been studied. Moreover, the tokens are rarely an end in itself: the same compressed representation is routinely reused for downstream clinical tasks such as classification, detection, and retrieval [37, 38], and increasingly serves as the input to multimodal and medical foundation models [39, 23, 24, 40], so whether quantization erases class-discriminative structure becomes a central criterion for selecting a tokenizer. Thus, compared to natural image tokenizers, the medical domain prioritizes two distinct goals over perfect pixel reconstruction: the latent representation must preserve the critical diagnostic features used by clinicians, and the subsequent generator must not compromise privacy by memorizing and reproducing exact patient scans. In this work we aim to close this gap. Our contributions are: • The first medical image tokenization benchmark: a controlled holistic evaluation of over sixty trained models. • A multi-axis evaluation protocol (reconstruction, generation, latent geometry, memorization, and downstream probing) revealing that natural image assumptions about reconstruction–generation correlation and latent space usage do not hold within our medical benchmark. • Reproducibility: open-source framework, all implementations, and trained tokenizer and generator weights, publicly released. Figure 2: Reconstruction predicts generation performance in medical imaging. Reconstruction versus generation performance of different tokenizers across compression factors and datasets, for natural images (left) and medical images (right); natural-image metrics are taken from prior work [28], exploiting different methods and backbones. Pearson and Spearman fits are overlaid. Results disentangled by dataset and compression factor are provided in the appendix (Appendix A), where the correlation holds within each stratum. Within our benchmark, reconstruction strongly predicts generation, in contrast to the natural-image trend. 2 Background and Related Work The variational autoencoder (VAE) [41] is the foundational framework for learned image compression: an encoder parameterizes a posterior qϕ(z|x)q_φ(z|x), a prior p(z)p(z) regularizes the latent space, and a decoder pθ(x|z)p_θ(x|z) reconstructs the input. Expressive decoders, however, can bypass the latent entirely (posterior collapse) by driving the Kullback-Leibler (KL) term to zero. VQ-VAE [42] avoids this by discretizing the bottleneck: an encoder E maps x to a continuous latent zez_e, quantized to zqz_q via nearest-neighbor lookup in a learned codebook =ekk=1KC=\e_k\_k=1^K, and a decoder D reconstructs from the result: ze z_e =E(x),zq=ek∗, =E(x), z_q=e_k^*, (1) k∗ k^* =argmink∥ze−ek∥2,x^=D(zq). = _k\|z_e-e_k\|_2, x=D(z_q). The KL term is replaced by a commitment loss ‖ze−sg[zq]‖22\|z_e-sg[z_q]\|_2^2 and a codebook loss ‖sg[ze]−zq‖22\|sg[z_e]-z_q\|_2^2, with sg[⋅]sg[·] the stop-gradient; as argmin is non-differentiable, gradients reach the encoder via the straight-through estimator (STE). VQ-GAN [43] adds adversarial and perceptual losses for sharper reconstructions. Vanilla VQ nonetheless suffers codebook collapse, where only a fraction of codes are used, as well as biased STE gradients. Subsequent work addresses these along several axes. Soft Quantization. Replacing the hard argmin with a differentiable weighted combination: zq=∑k=1Kwkek,wk≥0,∑kwk=1,z_q= _k=1^Kw_k\,e_k, w_k≥ 0,\;\; _kw_k=1, (2) bypasses the STE entirely. Methods differ in how wkw_k is set: Wu and Flierl [44] use Bayesian posterior-mean estimation over centroids, SCQ [45] solves for the optimal combination via a differentiable optimization layer, and SoftVQ-VAE [46] uses a temperature-scaled softmax over codebook similarities, wk∝exp(−∥ze−ek∥2/τ)w_k (-\|z_e-e_k\|^2/τ), recovering hard VQ as τ→0τ→ 0. This generalizes VQ-VAE’s K-means latent to soft K-means and, with data-dependent weights, to Gaussian mixtures [47], rendering codebook and commitment losses unnecessary. Space-filling (SF) methods [48, 49] instead quantize onto line segments between adjacent codes, zq=(1−γ)ej+γej+1z_q=(1-γ)\,e_j+γ\,e_j+1 with γ∈[0,1)γ∈[0,1), so neighboring codes encode similar content. Differentiable Quantization. An orthogonal line keeps the hard argmin in the forward pass but reparameterizes the output for richer encoder gradients. The STE, zq=ze+sg[ek∗−ze]z_q=z_e+sg[e_k^*-z_e], copies the decoder gradient unchanged, discarding the quantization step. NSVQ [50] instead substitutes magnitude-matched random noise for the quantization error. The rotation trick [51] builds a rotation-rescaling matrix M with ze=ek∗M\,z_e=e_k^* and sets zq=sg[]zez_q=sg[M]\,z_e, so the gradient ∂zq/∂ze=sg[]∂ z_q/∂ z_e=sg[M] encodes both angular and magnitude misalignment. DiVeQ [49] adds a simulated error vector via reparameterization, zq=ze+‖ze−ek∗‖2⋅u/‖u‖2z_q=z_e+\|z_e-e_k^*\|_2· u/\|u\|_2, with direction u aimed at the nearest codeword, keeping the forward pass identical to hard VQ. Lookup-Free Quantization. Lookup-free methods drop the explicit codebook, quantizing each latent dimension independently via per-dimension rounding zq=[q1(z1),…,qd(zd)]z_q=[q_1(z_1),…,q_d(z_d)] and eliminating collapse by construction. Finite scalar quantization (FSQ) [32] bounds each dimension via a tanh nonlinearity and rounds to one of LiL_i uniformly spaced integer levels, z^i=⌊Li−12tanh(zi)−oi⌉ z_i= L_i-12\, (z_i)-o_i , with oi=12o_i= 12 for even LiL_i and 00 otherwise, yielding an implicit codebook of size ∏i=1dLi _i=1^dL_i with no auxiliary losses. LFQ [52] takes Li=2L_i=2, binarizing via zq,i=sign(zi)∈−1,+1z_q,i=sign(z_i)∈\-1,+1\ for 2d2^d codes plus an entropy loss. Binary spherical quantization (BSQ) [53] refines LFQ by ℓ2 _2-normalizing the latent onto the unit hypersphere before binarization, which bounds the quantization error and yields a better-conditioned entropy objective. Codebook Reparameterization. These methods define codes through learned transformations so all entries receive gradients. SimVQ [34] factorizes the codebook as =C=WB via a learnable linear layer over a latent basis. QINCo [54] replaces it with an implicit neural codebook: at each residual stage an MLP fℓf_ generates the entries from the current reconstruction, ℓ=fℓ(z^ℓ−1)C_ =f_ ( z_ -1), so codes adapt per-sample and capture inter-stage dependencies. Residual and Product Quantization. These meta-schemes wrap any base quantizer to expand its capacity. Residual quantization (RQ) [55] quantizes the residual error over L stages: from r0=zer_0=z_e, each stage picks ekℓ=argmine∈ℓ‖rℓ−1−e‖2e_k_ = _e _ \|r_ -1-e\|_2 and updates rℓ=rℓ−1−ekℓr_ =r_ -1-e_k_ , giving zq=∑ℓ=1Lekℓz_q= _ =1^Le_k_ and up to KLK^L vectors. Product quantization (PQ) [56] partitions the latent into m subvectors and quantizes each independently, yielding (K′)m(K )^m codes from m×K′m× K centroids. Both are agnostic to the base quantizer, acting as composable building blocks. Table 1: Holistic reconstruction and generation overview. Cross-dataset central tendency over the 12 datasets, grouped by compression f. Cells report the mean, except rFMD/gFMD, which use the more robust median since Fréchet distances are sensitive to per-dataset sample counts (a few hundred to tens of thousands).↑ /↓ indicate better direction; FMD == Fréchet Medical Distance (each dataset uses its own feature extractor). Statistical and per-dataset specific results can be found in Appendices C and E. f=4f=4 f=8f=8 f=16f=16 Method PSNR↑ SSIM↑ rFID↓ rFMD↓ gFID↓ gFMD↓ PSNR↑ SSIM↑ rFID↓ rFMD↓ gFID↓ gFMD↓ PSNR↑ SSIM↑ rFID↓ rFMD↓ gFID↓ gFMD↓ AEKL [57] 30.2 0.823 47.4 1.67 76.2 22.4 30.8 0.826 47.5 1.43 73.9 18.5 30.6 0.809 55.9 2.01 88.8 21.0 SoftVQ [46] 34.4 0.911 21.9 0.23 79.9 20.2 30.2 0.817 50.4 1.27 107.9 38.9 32.2 0.820 48.1 0.93 113.6 10.1 VQGAN [43] 40.0 0.953 9.4 0.05 50.5 26.4 34.0 0.847 43.7 0.44 65.5 18.0 29.3 0.756 79.2 2.22 99.5 15.0 SimVQ [34] 39.1 0.946 11.7 0.09 49.4 14.9 34.8 0.885 24.0 0.19 63.2 31.5 28.8 0.762 82.2 2.86 111.8 34.0 SimQINCo [54] 40.1 0.953 9.5 0.10 52.3 28.0 35.0 0.877 26.6 0.41 52.8 19.2 31.6 0.797 64.5 0.99 91.5 33.2 RQVAE [55] 41.3 0.963 7.0 0.04 52.2 25.9 37.1 0.907 19.0 0.08 55.5 10.0 34.2 0.842 38.2 0.44 70.5 15.7 DiVeQ [49] 39.2 0.940 12.7 0.10 48.1 11.5 35.3 0.884 24.2 0.20 58.4 13.2 31.0 0.794 61.6 1.33 91.2 21.2 SF-DiVeQ [49] 38.8 0.943 12.4 0.04 48.7 26.1 35.8 0.892 22.7 0.19 58.8 17.1 31.3 0.793 57.0 1.18 83.7 11.2 BSQ [53] 30.5 0.860 33.5 0.82 104.5 35.6 27.7 0.808 54.5 2.48 81.5 26.4 27.7 0.773 67.9 2.45 102.5 21.2 LFQ [52] 29.4 0.860 40.1 0.94 141.9 56.0 24.0 0.708 103.8 13.37 226.1 38.7 23.2 0.655 148.0 19.24 138.5 31.9 3 Method We benchmark all tokenizers within a single autoencoding architecture [41], the de facto autoencoder underlying latent diffusion, ensuring our findings remain representative of deployed medical pipelines. We vary only the quantization module, holding the encoder, decoder, training budget, and data fixed. We first describe this shared autoencoder and the quantizers we plug into it (Sec. 3.1), then the generative model trained on the resulting latents (Sec. 3.2). 3.1 Autoencoder and Tokenization The encoder and decoder follow the convolutional VQ-GAN backbone [43] and realize Eq. (1): the encoder maps an image to a continuous latent zez_e, the quantizer discretizes it to zqz_q, and the decoder reconstructs the input. At each setting we fix the spatial compression factor f∈4,8,16f∈\4,8,16\ and the latent channel dimension d∈3,4,8d∈\3,4,8\, so every quantizer operates on latents of identical shape. We remove all self-attention, yielding a purely convolutional encoder-decoder. With backbone and optimization fixed, per-f differences are attributable to the quantizer alone. We omit self-attention, which the backbone instantiates only at certain resolutions (a subset of f), since its resolution-dependent global mixing would confound the cross-compression latent-geometry analysis (§5). Quantization Adaptations. Most quantizers are either designed for images or directly applicable. The exception is QINCo [54], built around an implicit neural codebook where a small MLP generates the codebook entries rather than storing them. As QINCo’s reconstruction-conditioned residual structure is computationally infeasible at image-tokenizer resolutions, we isolate the implicit codebook in a single-codebook variant named SimQINCo: the table ∈ℝK×dC ^K× d of a standard VQ layer is replaced by =gϕ(),C=g_φ(V), (3) a small shared MLP gϕg_φ applied to a learnable coordinate matrix ∈ℝK×dV ^K× d, thereby evaluating the implicit neural codebook in isolation. Training Objective. All tokenizers share an identical training objective combining a pixel-space Mean Squared Error (MSE) reconstruction term, a VGG-based LPIPS perceptual loss [58], a hinge adversarial loss [43] against a PatchGAN discriminator [59], and the quantizer-specific auxiliary loss ℒQL_Q (commitment, entropy, or codebook regularization) prescribed by each individual quantization scheme: ℒ=ℒMSE(x,x^)+λpℒLPIPS(x,x^)+λadvℒadv(x^)+ℒQ,L=L_MSE(x, x)+ _p\,L_LPIPS(x, x)+ _adv\,L_adv( x)+L_Q, (4) with λp=λadv=0.01 _p= _adv=0.01; the continuous AEKL baseline additionally minimizes a small KL term (λKL=10−6 _KL=10^-6). The perceptual term is linearly warmed up over the first 50k iterations. The adversarial term is held inactive for the first 100k steps and then linearly warmed up over a further 50k; thereafter its weight is adaptively rescaled by the gradient-norm ratio between ℒMSE+λpℒLPIPSL_MSE+ _pL_LPIPS and ℒadvL_adv [43]. Additionally, to stabilize discriminator training under the limited data scale typical of medical datasets, we additionally (i) apply differentiable augmentation (color, translation, cutout) to real and fake inputs [60], (i) include a consistency-regularization term (λCR=4 _CR=4) penalizing inconsistent logits under augmentation [61], and (i) add a LeCAM regularizer (λLeCAM=10−3 _LeCAM=10^-3) [62] on the discriminator’s real/fake logit EMAs. Figure 3: Codebook misalignment across quantization families. Joint t-SNE of the pre-quant latents zP_z (colored by source dataset) and the selected codewords zC_z (red crosses), pooled over the test split of all twelve datasets, one panel per family at f=8f=8; distortion-per-bit per-bit=/H()D_per-bit=D/H(C) is annotated top-left. Codewords lying on the latent cloud indicate good alignment; drift off it is the internal codebook covariate shift of Sec. 4.4. 3.2 Generation To assess each tokenizer as a generative substrate, we freeze the trained autoencoder and fit a single diffusion model in its continuous pre-quantization latent zez_e, rather than training an autoregressive transformer over the discrete zqz_q. The latter would entangle generation quality with codebook cardinality (the AR softmax scales as K, KLK^L, or 2d2^d across families), penalizing tokenizers for reasons unrelated to latent fidelity; the continuous zez_e is well-defined across all tokenizer families and admits a single shared generator, while also yielding a more robust inference pipeline since imperfectly denoised samples still snap to the correct codebook entry under the frozen quantizer, a property leveraged by state-of-the-art medical latent-diffusion systems [4, 63]. Following standard latent-diffusion practice [57], we therefore rescale every tokenizer’s zez_e by a single scalar (the reciprocal of its standard deviation, estimated once on the training split) so that all generators operate on unit-variance latents. Then, following the latent-diffusion and DDPM paradigm [57, 64], the forward process progressively corrupts a clean latent z0=E(x)z_0=E(x) with Gaussian noise according to a variance schedule βtt=1T\ _t\_t=1^T, q(zt∣z0) q(z_t z_0) =(zt,α¯tz0,(1−α¯t)), =N\! (z_t;\, α_t\,z_0,\,(1- α_t)\,I ), (5) α¯t α_t =∏s=1t(1−βs), = _s=1^t(1- _s), and a network ϵθ _θ is trained to predict the injected noise [64], ℒDM=z0,t,ϵ[∥ϵ−ϵθ(zt,t)∥22],ϵ∼(0,).L_DM=E_z_0,\,t,\,ε\! [\, ε- _θ(z_t,t) _2^2\, ], ε (0,I). (6) Sampling iteratively denoises zT∼(0,)z_T (0,I) back to z0z_0, which the frozen quantizer snaps to zqz_q before the decoder maps it to pixel space. Conditioning. We instantiate ϵθ _θ as a DiT-B/2 transformer [65]. Beyond the diffusion timestep t, the network is conditioned on two discrete signals: the class label y and the source-dataset index s, the latter through a learned dataset embedding that augments DiT’s standard timestep and class embeddings, so a single network is shared across all twelve datasets. Each signal is mapped to a dembd_emb-dimensional vector (ht,hy,hsh_t,h_y,h_s); unlike vanilla DiT, which sums the timestep and class embeddings, we concatenate the three into a single conditioning vector c=[ht;hy;hs]∈ℝ3dembc=[h_t;h_y;h_s] ^3d_emb, preventing the class and dataset factors from interfering in a shared additive code. Conditioning enters every block via AdaLN-Zero [65]: c regresses the shift, scale, and gate applied to the self-attention and MLP sublayers, with the modulation zero-initialized so each block starts at identity. 4 Experiments 4.1 Setup We benchmark eight discrete quantization families: VQGAN [43], SimVQ [34], SimQINCo [54], RQVAE [55], DiVeQ [49], SF-DiVeQ [49], LFQ [52], and BSQ [53], together with continuous AEKL [57] and soft SoftVQ [46] baselines. Each method is trained at three spatial compression factors f∈4,8,16f∈\4,8,16\ on the twelve 2D datasets of the MedMNIST+ collection [66] at their native 224×224224× 224 resolution resulting in over 700,000 expert-labeled clinical images spanning pathology, radiology, dermatology, ophthalmology, and microscopy, with multi-class, multi-label, and ordinal classification tasks. Following Sec. 3, every tokenizer uses the identical encoder-decoder backbone, loss weights, and training schedule; only the quantizer and compression factor vary, so all observed differences are attributable to the quantization scheme. Both stages, the tokenizer and its DiT-B/2 generator, are trained on 2× NVIDIA H100 GPUs for two days each. For image generation, we use 100 sampling steps on a linear schedule, following [64]. 4.2 Reconstruction and Generation We evaluate each tokenizer in two regimes. For reconstruction, we encode and decode every test image and report PSNR, SSIM, LPIPS [58], and reconstruction-FID (rFID) against the ground truth using torch-fidelity [67]. For generation, we freeze the autoencoder, train a single DiT-B/2 diffusion model [65] on its continuous latents (Sec. 3.2), sample per dataset as many images as its test split (conditioned on the dataset and, where applicable, class embedding to match the test-split class distribution) and report generation-FID (gFID). Since both FIDs use an ImageNet-trained Inception-V3 backbone that is poorly calibrated to medical images, we additionally report FMD, which swaps this backbone for the benchmark’s official per-dataset ResNet-18 baseline classifier [66] (head removed) so the distance is measured in a feature space tuned to each dataset. We compute it in both regimes as a domain-aware counterpart to rFID and gFID. 4.3 Codebook Metrics We characterize the discrete bottleneck from the per-code selection counts ckc_k accumulated over the entire test split, with empirical probabilities pk=ck/∑jcjp_k=c_k/ _jc_j over a codebook of size K. Usage U=1K∑k=1K[ck>0]U= 1K _k=1^K1[c_k>0] is the fraction of codes ever selected, and normalized entropy H~=H()/log2K H=H(C)/ _2K, with H()=−∑k=1Kpklog2pkH(C)=- _k=1^Kp_k _2p_k, measures how evenly information is spread across the codebook. To probe how the latent space is used, we additionally report the stable rank of the centered pre-quant latents ∈ℝN×dZ ^N× d, computed from their singular values σ1≥⋯≥σd _1≥…≥ _d as sr()=(∑iσi2)/σ12∈[1,d]sr(Z)=( _i _i^2)/ _1^2∈[1,d], which counts the effective number of dimensions used. 4.4 Codebook Misalignment To visualize the relationship between the codebook and the latent distribution it quantizes, we encode the test images of all twelve datasets to their pre-quant latents z=znP_z=\z_n\, pool them, and collect the codewords actually selected, zC_z. We embed z∪zP_z _z jointly with t-SNE and plot both in the shared 2D space, which exposes two failure modes: codebook collapse, where only a small fraction of codewords is ever selected (a sparse zC_z), and internal codebook covariate shift, where the used codes drift off the latent cloud they are meant to cover. We quantify the associated rate–distortion efficiency with the distortion-per-bit per-bit=/H()D_per-bit=D/H(C), where =1N∑n=1N∥zn−zq,n∥22D= 1N _n=1^N z_n-z_q,n _2^2 is the mean quantization error between the pre-quant latent znz_n and its quantized value zq,nz_q,n (the cumulative sum over residual stages, where applicable) and H()=∑ℓ=1LH(ℓ)H(C)= _ =1^LH(C_ ) is the empirical code-usage entropy. Charging distortion against the bits actually used rather than the allocated budget B=∑ℓ=1Llog2KℓB= _ =1^L _2K_ (Tab. S6) penalizes collapse directly and prevents a larger codebook from appearing efficient, following [49]. 4.5 Correlation To test whether reconstruction predicts generation, we compute both Pearson and Spearman correlations across all model configurations. The Pearson coefficient r=Cov(X,Y)/(σXσY)r=Cov(X,Y)/( _X _Y) captures linear association, while the Spearman coefficient ρ=1−6∑iδi2/[n(n2−1)]ρ=1-6 _i _i^2/[\,n(n^2-1)\,], with δi=rank(xi)−rank(yi) _i=rank(x_i)-rank(y_i), captures monotonic rank agreement and is robust to FID’s heavy-tailed scale; reporting both guards against a single outlier family driving the trend. We attach 95% confidence intervals via the non-parametric bootstrap (B=10,000B=10,000 resamples with replacement, 2.52.5th/97.597.5th percentiles), which is rank- and distribution-free and thus well-suited to FID’s heavy-tailed scale and our moderate sample size of a few hundred (tokenizer, dataset) pairs. Figure 4: Codebook utilization and latent geometry are decoupled. Three tokenizer properties grouped by family and compression. Modern schemes reach near-full codebook utilization (mid) yet collapse their latents onto a thin, low-rank subspace (bottom), showing that a fully used codebook does not imply an expressive latent space and that codebook usage alone is a misleading indicator of tokenizer quality. Discretization largely preserves downstream-useful information (top). Figure 5: Memorization is mild and weakens under stronger compression. Columns: SSCD (copy-detection) and DINOv2 (semantic) extractors. Top: copy-rate vs. compression factor f, with one point per (family, dataset) and black bars denoting per-f means. Rates remain far below the real-data baseline (dashed) and decrease as the bottleneck tightens. The N-distance ratio stays well under the ”no single match” line. 4.6 Memorization To test whether a tokenizer’s bottleneck leaks training data, we adopt a nearest-neighbor replication test in the spirit of Somepalli et al. [68]. For each (tokenizer, dataset) configuration we embed every generated image and, as a calibrated reference, every held-out test image, and retrieve their nearest neighbors in the full training set. Embeddings come from two complementary encoders: SSCD [69], purpose-built for copy detection, and DINOv2 [70], which captures higher-level semantic similarity; a configuration is flagged only when both agree. We report copy-rate, the fraction of generated images whose top-1 training similarity exceeds the 9595th percentile of the test-to-train similarity distribution, a per-dataset threshold that makes the real held-out data its own baseline (≈0.05≈ 0.05 by construction), so that values above baseline indicate copying beyond what genuinely novel images exhibit. As a complementary view we also report the distance ratio between each generated image’s nearest and its next-k training neighbors (k=50k=50), where values near one indicate no single memorized match. We cap each dataset at 10,00010,000 generated images and compare against the complete training split. 4.7 Semantics and Downstream Evaluation To test if quantization preserves the semantically useful information needed for downstream tasks, we evaluate each frozen tokenizer through linear probing on the datasets’ labeled classes. For every model we extract two representation variants, the continuous pre-quantization latent zez_e and its quantized counterpart zqz_q, both flattened across the spatial dimensions into a single feature vector and standardized to zero mean and unit variance. On top of each variant, we fit a single linear classifier for 50 epochs with the tokenizer held frozen, select the best checkpoint on the validation split, and report test performance under each dataset’s task-appropriate primary metric (top-1 accuracy for multi-class tasks, macro-AUROC for multi-label tasks, and quadratic-weighted kappa for the ordinal grading task). The per-dataset gap Δ=M(ze)−M(zq) =M(z_e)-M(z_q) in the primary metric MM quantifies the change in class-discriminative structure across the discretization step itself, isolating the effect of quantization from the encoder’s representation capacity. 5 Results and Discussion Reconstruction and generation performance in medical imaging strongly correlate. Across all configurations, reconstruction metrics are strongly predictive of generation quality: rFID and gFID correlate at r=0.82r=0.82 with 95%95\% bootstrap CI [0.77,0.86][0.77,0.86] (B=10,000B=10,000 resamples over n=360n=360 paired observations; Spearman ρ=0.81[0.77,0.85]ρ=0.81\,[0.77,0.85]) (Fig. 2), and PSNR/LPIPS show the same trend (per-method values in Tab. 1). Moreover, Appendix A disentangles the correlation by dataset and by compression factor, showing it is not an artifact of pooling since the same relationship holds across each stratum. This contrasts with reported natural-image results, where reconstruction is a poor proxy for generation [27, 28, 29]. We conjecture this reflects the distinct statistics of medical data, stronger anatomical priors, lower intra-class variance, and limited texture diversity, which yield latent spaces whose reconstructability and generative modelability move together; whether representation-aligned tokenizers would follow a different regime remains open. This is practically valuable since judging a tokenizer by generation requires training a generator per configuration while reconstruction is free from the autoencoder, the correlation lets practitioners select tokenizers and search architectures using rFID alone, reserving generator training for a shortlist. It further makes reconstruction a legitimate optimization target, since reducing reconstruction error is expected to improve generation. Decoupled codebook usage and latent geometry. Nearly every modern scheme cures the canonical VQ collapse: as f grows from 44 to 1616, VQGAN usage falls from 79%79\% to 1.2%1.2\%, yet reparameterized (SimVQ, SimQINCo), residual (RQVAE), and lookup-free (LFQ, BSQ) methods all hold ≈100%≈ 100\% utilization (Fig. 4; only SF-DiVeQ and SoftVQ collapse partially). But high usage does not imply an efficient latent space: explicit-codebook methods, even at full utilization, compress their latents onto a thin, anisotropic subspace (stable rank 0.150.15–0.540.54 of d), whereas lookup-free (0.550.55–0.870.87) and continuous (0.830.83–0.970.97) methods stay near-isotropic. This could be driven by the general quantization scheme, not the data or the gradient estimator: nearest-neighbor lookup lets the encoder collapse onto a low-rank manifold the codebook can cover, and it is no straight-through artifact, since DiVeQ propagates true gradients through the quantizer yet collapses just like the rest. The immediate consequence is definitional: since the encoder packs information into a fraction of the available dimensions, the nominal latent dimensionality overstates how much of the space each tokenizer actually uses. Beyond this, the collapse appears benign; stable rank shows no clear effect on either reconstruction or generation, so we treat it as an intrinsic geometric property of these quantizers and an axis independent of downstream quality rather than a driver of it. Codebook collapse and misalignment. A joint t-SNE of the pre-quant latents zP_z and the selected codes zC_z (Fig. 3) serves as a more diagnostic read-out of tokenizer quality than codebook usage alone, capturing both how much of the codebook a model uses and how well it places that codebook onto the data manifold. It reveals that usage and geometric alignment with the data are independent axes, and that each family trades them off in a distinct way. Vanilla VQGAN displays the canonical codebook collapse pattern: only a few live codewords concentrate tightly on the densest region of zP_z and reconstruct what they cover at low distortion, but most codewords go unused, leaving most of the latent cloud unreached. Lookup-free schemes (LFQ, BSQ) sit at the opposite extreme: their implicit codebooks spread broadly across the embedding space, yielding nearly full usage but settling far from the data manifold, which translates to high quantization error despite the healthy utilization numbers. Codebook-reparameterization methods fall in between: SimVQ exhibits a usage shift in which some datasets are covered densely while others are left sparse, whereas SimQINCo blankets all twelve datasets uniformly and at lower distortion than SimVQ. The differentiable schemes achieve both wide coverage and low distortion, with DiVeQ attaining the lowest per-bitD_per-bit among the single-codebook methods; SF-DiVeQ, despite interpolating along codeword segments, does not improve on it here. Residual quantization (RQVAE) attains the lowest distortion overall, though at a higher bit rate (Tab. S6), so its low per-bitD_per-bit partly reflects a higher operating rate. Memorization is mild and decreases under stronger compression. A tokenizer that reproduces its training data undermines the privacy argument for synthetic imaging, so we ask whether the tokenizer leaks data. Fig. 5 shows it largely does not: across all 720720 configurations mean copy-rate stays well below the real-data baseline, and the nearest-neighbor distance ratio remains near one, meaning generated images sit in generic high-density regions rather than locking onto any single example. Outright replication is rare, so on aggregate the bottleneck withholds identity as required. This is not an underfitting artifact as copy-rate is essentially uncorrelated with generation quality and the few elevated copy-rates come from the best generators (Fig. S11). The exceptions concentrate on Path and OCT, for partly different reasons (Tab. S21). Path is among the least diverse datasets by every measure (low effective rank, low pairwise distance, high nearest-neighbor similarity), so its near-duplicate scans leave a generator little room for novelty. OCT only looks diverse in raw pixels, where speckle inflates variance; its B-scans share a stereotyped layered structure and stay semantically repetitive. Thus, memorization is rather driven by data than by tokenizer design. The only design choice that matters is compression: memorization falls steadily as the bottleneck tightens, because a coarser latent simply cannot carry the detail that makes a sample traceable. This is the same trade-off we see on our other axes: the compression that protects privacy also discards diagnostic and representational signal. Discretization largely preserves downstream-useful information. Finally, we probe how much semantically useful information survives quantization by training linear classifiers on the frozen latents (Tab. S20). Discretization is largely information-preserving: for explicit-codebook (VQGAN, SimVQ, SimQINCo), residual (RQVAE), and differentiable (DiVeQ, SF-DiVeQ) schemes the probe gap Δ=M(ze)−M(zq) =M(z_e)-M(z_q) is statistically indistinguishable from zero, i.e. the discrete latent zqz_q matches the continuous bottleneck zez_e to within noise. The exception is the lookup-free family (LFQ, BSQ), whose per-dimension binarization incurs a consistent gap (Δ≈0.02 ≈ 0.02–0.050.05) across all three compression factors. Strikingly, this is independent of latent rank: lookup-free latents are the highest-rank of all families (Sec. 5), yet lose the most downstream-useful structure—so the erosion stems from the hard scalar quantization grid, not from the low-rank geometry of explicit-codebook methods. Downstream utility is thus a largely separate axis from reconstruction and generation, one on which most quantizers are safe and only lookup-free binarization pays a price, a consideration absent from natural-image tokenizer design. Summary: Practitioner’s Guide in medical imaging. Under our evaluated setting we observe: • Reconstruction still has headroom. Reconstruction has not yet saturated and, since it tends to predict generation (r=0.82r=0.82), it appears to be a reasonable lever to keep improving, with limited privacy risk given that memorization remains mild in our experiments. • Discrete tokenizers are competitive substrates for continuous-latent diffusion. In our setup, discrete tokenizers tend to match or outperform the continuous baseline on reconstruction and generation while preserving downstream utility comparably. • Residual quantization is a strong default. For a favorable compute-to-performance trade-off, residual quantization (RQVAE) is a reasonable first choice, performing well across compression factors with little tuning. 6 Conclusion Within our benchmark, medical image tokenization departs from natural-image expectations. The field’s inherited assumptions break: reconstruction predicts generation, a healthy codebook hides a collapsed latent, and discretization is largely free for both privacy and downstream use. Within this setting, there is no single winner, but a clear practitioner’s guide emerges, and reconstruction remains a lever worth pushing. Limitations and Future Work. Our study covers only 2D medical data. Higher-resolution and volumetric data, where compression and memory constraints differ, remain unexplored. We assess each tokenizer through a continuous-latent diffusion model rather than autoregressive modeling of the discrete codes, with a single fixed DiT-B/2 generator, so generation quality reflects latent fidelity but not code-sequence learnability or generator capacity. Downstream utility is gauged via linear probing, a deliberately simple proxy for richer clinical tasks. Our natural-versus-medical comparison also relies on reported natural-image numbers rather than a matched control, which we leave to future work alongside representation-aligned tokenizers. Looking forward, the decoupling of codebook usage from latent geometry suggests designing quantizers that target the latent-rank axis directly rather than chasing utilization. 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PSNR correlates negatively (higher PSNR → lower/better gFID). Dataset Pearson r [95% CI] Spearman ρ [95% CI] Path −0.63-0.63 [−0.78,−0.37][-0.78,-0.37] −0.67-0.67 [−0.85,−0.38][-0.85,-0.38] Chest −0.73-0.73 [−0.89,−0.65][-0.89,-0.65] −0.89-0.89 [−0.95,−0.73][-0.95,-0.73] Derma −0.76-0.76 [−0.88,−0.59][-0.88,-0.59] −0.74-0.74 [−0.86,−0.50][-0.86,-0.50] OCT −0.76-0.76 [−0.92,−0.59][-0.92,-0.59] −0.82-0.82 [−0.94,−0.57][-0.94,-0.57] Pneu −0.51-0.51 [−0.70,−0.18][-0.70,-0.18] −0.43-0.43 [−0.69,−0.07][-0.69,-0.07] Reti −0.72-0.72 [−0.84,−0.54][-0.84,-0.54] −0.77-0.77 [−0.87,−0.57][-0.87,-0.57] Breast −0.83-0.83 [−0.91,−0.71][-0.91,-0.71] −0.89-0.89 [−0.95,−0.74][-0.95,-0.74] Blood −0.57-0.57 [−0.75,−0.34][-0.75,-0.34] −0.57-0.57 [−0.75,−0.26][-0.75,-0.26] Tiss −0.66-0.66 [−0.80,−0.47][-0.80,-0.47] −0.63-0.63 [−0.78,−0.36][-0.78,-0.36] OrgA −0.82-0.82 [−0.91,−0.72][-0.91,-0.72] −0.88-0.88 [−0.94,−0.70][-0.94,-0.70] OrgC −0.78-0.78 [−0.87,−0.67][-0.87,-0.67] −0.84-0.84 [−0.91,−0.69][-0.91,-0.69] OrgS −0.76-0.76 [−0.85,−0.66][-0.85,-0.66] −0.80-0.80 [−0.88,−0.64][-0.88,-0.64] Pooled −0.67-0.67 [−0.71,−0.64][-0.71,-0.64] −0.74-0.74 [−0.79,−0.69][-0.79,-0.69] Table S3: Per-dataset correlation of rFID with DiT-B/2 generation-FID, with 95%95\% bootstrap CIs (B=10,000B=10,000). n=30n=30 (tokenizer, compression) configs per dataset; pooled n=360n=360. rFID correlates positively with gFID across every dataset. Dataset Pearson r [95% CI] Spearman ρ [95% CI] Path +0.61+0.61 [+0.17,+0.84][+0.17,+0.84] +0.54+0.54 [+0.17,+0.78][+0.17,+0.78] Chest +0.79+0.79 [+0.73,+0.97][+0.73,+0.97] +0.87+0.87 [+0.69,+0.95][+0.69,+0.95] Derma +0.75+0.75 [+0.60,+0.90][+0.60,+0.90] +0.76+0.76 [+0.55,+0.87][+0.55,+0.87] OCT +0.80+0.80 [+0.67,+0.98][+0.67,+0.98] +0.93+0.93 [+0.79,+0.98][+0.79,+0.98] Pneu +0.48+0.48 [+0.07,+0.76][+0.07,+0.76] +0.38+0.38 [+0.06,+0.63][+0.06,+0.63] Reti +0.82+0.82 [+0.59,+0.93][+0.59,+0.93] +0.77+0.77 [+0.55,+0.88][+0.55,+0.88] Breast +0.92+0.92 [+0.84,+0.97][+0.84,+0.97] +0.92+0.92 [+0.82,+0.96][+0.82,+0.96] Blood +0.42+0.42 [+0.11,+0.80][+0.11,+0.80] +0.42+0.42 [+0.10,+0.65][+0.10,+0.65] Tiss +0.71+0.71 [+0.24,+0.95][+0.24,+0.95] +0.65+0.65 [+0.35,+0.83][+0.35,+0.83] OrgA +0.77+0.77 [+0.62,+0.92][+0.62,+0.92] +0.87+0.87 [+0.69,+0.95][+0.69,+0.95] OrgC +0.72+0.72 [+0.53,+0.88][+0.53,+0.88] +0.79+0.79 [+0.62,+0.89][+0.62,+0.89] OrgS +0.69+0.69 [+0.49,+0.87][+0.49,+0.87] +0.74+0.74 [+0.54,+0.85][+0.54,+0.85] Pooled +0.82+0.82 [+0.77,+0.86][+0.77,+0.86] +0.81+0.81 [+0.77,+0.85][+0.77,+0.85] Table S4: Per-compression correlation of PSNR with DiT-B/2 generation-FID, with 95% bootstrap CIs (B=10,000B=10,000). PSNR correlates negatively (higher PSNR → lower/better gFID) at every compression. Compression Pearson r [95% CI] Spearman ρ [95% CI] f=4f=4 −0.68-0.68 [−0.75,−0.61][-0.75,-0.61] −0.73-0.73 [−0.80,−0.64][-0.80,-0.64] f=8f=8 −0.72-0.72 [−0.78,−0.66][-0.78,-0.66] −0.79-0.79 [−0.85,−0.70][-0.85,-0.70] f=16f=16 −0.61-0.61 [−0.69,−0.52][-0.69,-0.52] −0.62-0.62 [−0.73,−0.48][-0.73,-0.48] Pooled −0.67-0.67 [−0.71,−0.64][-0.71,-0.64] −0.74-0.74 [−0.79,−0.69][-0.79,-0.69] Table S5: Per-compression correlation of rFID with DiT-B/2 generation-FID, with 95% bootstrap CIs (B=10,000B=10,000). rFID correlates positively with gFID at every compression, and the association strengthens as the bottleneck tightens. Compression Pearson r [95% CI] Spearman ρ [95% CI] f=4f=4 +0.71+0.71 [+0.63,+0.78][+0.63,+0.78] +0.76+0.76 [+0.68,+0.82][+0.68,+0.82] f=8f=8 +0.86+0.86 [+0.81,+0.91][+0.81,+0.91] +0.88+0.88 [+0.82,+0.91][+0.82,+0.91] f=16f=16 +0.90+0.90 [+0.84,+0.94][+0.84,+0.94] +0.85+0.85 [+0.76,+0.91][+0.76,+0.91] Pooled +0.82+0.82 [+0.77,+0.86][+0.77,+0.86] +0.81+0.81 [+0.77,+0.85][+0.77,+0.85] Figure S6: The reconstruction–generation coupling strengthens with compression. Reconstruction metric vs. DiT-B/2 gFID per compression factor (n=120n=120 each). Top: rFID; bottom: PSNR. Pearson OLS (95%95\% band) and Spearman fits, with r [95%[95\% CI]] and ρ inset. The coupling tightens as f=→16f=4\!→\!8\!→\!16. Figure S7: Reconstruction predicts generation within every dataset. Per-dataset scatter of a reconstruction metric against DiT-B/2 gFID, one panel per MedMNIST+ dataset (n=30n=30 (tokenizer, compression) configs each), colored by tokenizer family and marked by compression factor. Left block: rFID; right block: PSNR. Each panel overlays a Pearson OLS fit (with a 95%95\% band) and a Spearman monotone fit; the inset box reports Pearson r [95%[95\% CI]] and Spearman ρ. rFID correlates positively and PSNR negatively with gFID in all twelve datasets, confirming that the pooled trend is not an artifact of aggregation. Appendix B Bit-Compression While we aim to keep the bit budget comparable across quantizers, some variation is inevitable, since each family encodes its latents differently: single-codebook methods spend one index per token, RQVAE spends several across its residual stages, and lookup-free schemes spend one bit per latent dimension. Table S6 lists the resulting per-token budget B for each family, which we use to normalize distortion into the distortion-per-bit per-bit=/BD_per-bit=D/B of Sec. 4.4. Table S6: Per-token bit budget B=∑ℓ=1Llog2KℓB= _ =1^L _2K_ used to normalize distortion, per-bit=/BD_per-bit=D/B (Sec. 4.4). Single-codebook families spend one index (B=log2KB= _2K, L=1L=1); RQVAE uses L=4L=4 residual stages of size K; lookup-free families spend one bit per latent dimension (B=dB=d). Codebooks are K=8192K=8192 at f=4f=4 and K=16384K=16384 at f=8,16f=8,16. AEKL is continuous (no discrete budget); SoftVQ’s budget is nominal as its assignment is soft. Family (B) f=4f=4 f=8f=8 f=16f=16 VQGAN (log2K _2K) 13 14 14 SimVQ (log2K _2K) 13 14 14 SimQINCo (log2K _2K) 13 14 14 DiVeQ (log2K _2K) 13 14 14 SF-DiVeQ (log2K _2K) 13 14 14 RQVAE (4log2K4 _2K) 52 56 56 LFQ (d) 10 14 18 BSQ (d) 10 14 18 Appendix C Quantitative Reconstruction We report pixel and perceptual fidelity per dataset—PSNR (Tab. S7), SSIM (Tab. S8), LPIPS (Tab. S9), and pixel-MSE (Tab. S10)—together with reconstruction-FID (Tab. S11). RQVAE is the strongest reconstructor on nearly every dataset and compression factor, whereas the lookup-free families (LFQ, BSQ) trail throughout and degrade sharply at f=16f=16. Table S7: Per-dataset PSNR (↑ ). Cells: mean±σmean_±σ over test images. Method Path Chest Derma OCT Pneu Reti Breast Blood Tiss OrgA OrgC OrgS mean f=4f=4 AEKL 25.4±3.1 31.1±1.3 30.3±2.0 27.5±1.6 30.7±1.5 31.0±1.6 26.8±1.1 30.6±1.9 38.5±2.0 30.3±2.6 30.3±3.2 30.5±3.2 30.2 SoftVQ 28.1±3.1 36.2±1.6 32.0±2.2 29.6±1.8 35.8±1.8 31.2±2.5 30.6±1.3 33.8±1.2 47.0±2.2 36.3±3.9 36.0±4.3 36.4±4.2 34.4 VQGAN 31.1±3.4 41.4±1.5 37.1±2.1 32.4±2.0 40.8±1.5 39.4±1.4 35.7±1.3 38.1±1.8 53.8±0.8 43.6±4.4 43.0±4.7 43.5±4.7 40.0 SimVQ 30.0±3.5 41.1±1.6 36.8±2.2 31.8±2.0 40.6±1.8 38.1±1.5 34.3±1.4 37.0±1.8 52.2±1.6 42.9±4.8 42.1±5.1 42.6±5.1 39.1 SimQINCo 31.4±3.8 42.1±1.4 37.7±1.9 32.4±2.1 41.1±1.5 39.2±1.3 35.7±1.4 37.8±1.6 52.6±1.6 44.0±4.2 43.1±4.5 43.6±4.5 40.1 RQVAE 31.9±3.5 43.1±1.6 39.1±2.2 33.4±2.1 42.5±1.6 39.0±1.4 37.0±1.4 38.2±1.4 55.3±0.9 45.8±4.2 45.2±4.8 45.5±4.7 41.3 DiVeQ 29.9±3.9 40.5±1.6 37.1±2.2 31.4±2.0 40.0±1.9 39.2±1.3 34.0±1.3 37.4±1.9 52.9±1.6 43.0±5.3 42.3±5.6 42.9±5.5 39.2 SF-DiVeQ 29.8±3.5 40.4±1.6 36.2±2.1 31.6±2.0 39.9±1.8 36.6±1.9 33.8±1.4 37.1±1.8 52.9±1.9 42.6±5.0 41.9±5.4 42.5±5.3 38.8 BSQ 24.7±3.0 31.4±1.5 29.4±2.2 27.8±1.5 31.5±1.7 29.8±2.1 27.2±1.3 30.6±1.8 42.6±2.6 30.4±3.2 30.1±3.5 30.5±3.5 30.5 LFQ 24.4±3.1 30.6±1.6 27.7±2.7 26.9±1.6 30.5±1.8 27.4±2.4 26.2±1.2 30.5±2.1 40.5±3.9 29.4±2.5 29.0±2.9 29.3±2.8 29.4 f=8f=8 AEKL 25.0±3.1 31.8±1.3 30.9±1.9 27.6±1.6 31.4±1.5 31.5±1.4 26.9±1.1 31.0±1.7 39.8±1.7 31.2±3.3 31.1±3.7 31.4±3.6 30.8 SoftVQ 24.2±3.5 31.5±1.6 30.6±2.1 27.2±1.5 31.8±1.7 29.2±1.8 26.1±1.4 30.8±2.1 41.3±2.5 29.9±3.1 29.9±3.7 30.2±3.5 30.2 VQGAN 24.8±3.9 35.4±1.9 33.3±2.2 28.4±1.8 34.9±2.1 35.0±1.5 27.9±1.6 32.7±2.6 51.0±1.4 34.9±6.4 34.8±6.9 35.5±6.9 34.0 SimVQ 26.6±3.9 36.0±1.5 34.8±2.3 29.4±1.9 35.4±1.8 36.2±1.6 29.7±1.4 34.4±2.3 49.0±2.4 35.6±4.6 35.3±5.0 35.8±5.0 34.8 SimQINCo 26.2±3.9 36.6±1.7 34.7±2.4 29.0±1.8 36.2±2.1 35.0±1.4 29.5±1.5 34.3±2.4 48.5±1.2 36.6±5.6 36.6±6.4 37.2±6.3 35.0 RQVAE 27.6±3.9 38.0±1.7 35.8±2.3 29.9±1.9 37.5±2.0 36.6±1.4 30.8±1.5 35.7±2.1 53.8±0.8 40.1±6.5 39.1±6.6 39.8±6.6 37.1 DiVeQ 26.4±4.0 36.6±1.7 34.5±2.2 29.3±1.9 36.1±2.0 35.9±1.6 29.4±1.5 34.3±2.4 50.8±1.9 37.0±5.8 36.5±6.2 37.2±6.2 35.3 SF-DiVeQ 27.2±4.2 37.5±1.8 35.5±2.4 29.6±1.9 36.6±2.0 37.4±1.3 30.3±1.4 35.2±2.3 49.2±2.1 37.2±5.1 37.0±5.7 37.5±5.6 35.8 BSQ 22.5±3.0 29.0±1.4 26.7±2.2 26.5±1.4 28.6±1.6 27.1±2.4 24.7±1.4 28.0±1.9 38.0±3.0 27.0±2.6 27.0±3.1 27.3±3.0 27.7 LFQ 20.0±2.9 25.7±2.0 24.2±3.0 24.4±1.6 24.8±1.9 24.8±2.2 20.2±2.1 24.2±2.3 33.2±3.9 22.2±2.5 22.0±2.9 22.2±3.0 24.0 f=16f=16 AEKL 24.3±3.6 32.0±1.4 31.2±1.9 27.4±1.6 31.4±1.6 30.0±1.5 26.5±1.3 30.9±2.3 40.5±1.6 30.8±3.5 30.8±4.1 31.2±4.0 30.6 SoftVQ 24.5±4.0 34.1±1.6 32.6±2.4 28.2±1.7 33.6±2.0 33.3±1.6 26.3±1.5 32.1±2.6 44.6±2.3 32.3±4.7 32.1±5.3 32.7±5.3 32.2 VQGAN 22.4±4.3 31.2±1.8 31.2±2.5 27.5±1.6 30.6±2.0 30.2±1.6 24.5±1.7 28.9±2.7 41.2±2.6 27.5±3.5 27.8±4.5 28.1±4.5 29.3 SimVQ 22.7±4.0 30.2±1.6 30.5±2.3 27.0±1.5 29.6±1.7 30.1±1.3 24.4±1.5 29.0±2.6 39.0±2.6 27.3±3.2 27.6±4.1 27.9±4.0 28.8 SimQINCo 23.6±4.5 33.2±1.8 32.9±2.6 28.0±1.7 32.6±2.1 34.1±1.3 25.8±1.6 31.0±3.0 46.1±2.4 30.3±4.4 30.7±5.5 31.1±5.4 31.6 RQVAE 25.2±4.3 35.5±1.9 33.9±2.5 28.6±1.9 34.6±2.1 35.0±1.4 27.6±1.6 33.0±2.7 52.6±1.5 34.7±6.3 34.5±6.9 35.2±6.8 34.2 DiVeQ 23.5±4.4 32.7±1.7 31.9±2.3 28.0±1.7 32.0±2.1 30.8±1.0 25.5±1.6 30.8±2.9 45.5±2.6 29.9±4.2 30.2±5.3 30.6±5.2 31.0 SF-DiVeQ 23.5±4.3 33.0±1.8 32.4±2.4 28.0±1.7 32.4±2.0 33.8±1.4 25.7±1.6 30.8±3.0 44.6±2.5 30.1±4.2 30.4±5.4 30.8±5.2 31.3 BSQ 22.1±3.4 29.1±1.7 28.4±2.4 26.0±1.5 28.9±1.9 28.2±2.3 24.0±1.3 27.9±2.2 38.2±3.0 26.3±2.9 26.5±3.7 26.7±3.5 27.7 LFQ 19.1±3.6 24.6±1.9 23.8±2.6 22.4±1.6 24.5±1.9 24.2±2.1 20.2±1.5 23.6±2.0 32.0±3.2 21.2±2.4 21.1±2.9 21.4±2.8 23.2 Table S8: Per-dataset SSIM (↑ ). Cells: mean±σmean_±σ over test images. Method Path Chest Derma OCT Pneu Reti Breast Blood Tiss OrgA OrgC OrgS mean f=4f=4 AEKL .714±.119 .883±.027 .838±.057 .578±.088 .854±.031 .887±.024 .707±.027 .891±.035 .965±.009 .856±.091 .848±.102 .857±.100 .823 SoftVQ .846±.068 .953±.011 .907±.031 .700±.066 .939±.012 .938±.027 .852±.021 .935±.017 .993±.003 .961±.039 .954±.047 .957±.044 .911 VQGAN .906±.049 .981±.004 .943±.019 .832±.038 .973±.006 .960±.021 .941±.008 .954±.015 .997±.000 .986±.016 .983±.024 .985±.021 .953 SimVQ .884±.059 .977±.006 .937±.022 .808±.045 .968±.007 .961±.013 .926±.010 .950±.016 .997±.001 .984±.023 .979±.031 .980±.028 .946 SimQINCo .905±.055 .983±.004 .946±.019 .828±.040 .975±.006 .949±.019 .941±.008 .955±.015 .997±.001 .987±.016 .984±.025 .985±.022 .953 RQVAE .921±.044 .986±.003 .951±.017 .865±.033 .980±.004 .962±.015 .958±.007 .959±.014 .998±.000 .992±.010 .989±.017 .991±.015 .963 DiVeQ .869±.068 .975±.007 .932±.024 .785±.049 .964±.008 .966±.011 .916±.011 .949±.017 .997±.000 .980±.029 .976±.037 .978±.034 .940 SF-DiVeQ .879±.058 .977±.006 .935±.022 .798±.046 .966±.007 .965±.019 .918±.011 .949±.016 .998±.000 .980±.025 .976±.032 .978±.030 .943 BSQ .743±.100 .912±.021 .873±.043 .670±.067 .893±.025 .882±.034 .771±.021 .901±.032 .985±.009 .903±.069 .888±.079 .895±.077 .860 LFQ .755±.096 .903±.024 .866±.043 .666±.063 .887±.026 .900±.033 .784±.023 .903±.030 .982±.008 .895±.061 .887±.074 .893±.071 .860 f=8f=8 AEKL .679±.140 .892±.026 .837±.057 .576±.089 .861±.030 .913±.023 .701±.029 .892±.036 .972±.008 .867±.100 .856±.110 .867±.107 .826 SoftVQ .636±.159 .894±.027 .854±.055 .582±.086 .875±.031 .902±.021 .667±.039 .887±.040 .982±.007 .850±.106 .836±.119 .842±.119 .817 VQGAN .644±.163 .929±.020 .866±.053 .601±.087 .898±.026 .942±.017 .727±.037 .897±.041 .996±.001 .895±.103 .879±.117 .889±.115 .847 SimVQ .741±.122 .945±.014 .890±.042 .672±.073 .922±.020 .947±.019 .811±.025 .922±.027 .996±.001 .930±.078 .920±.085 .926±.081 .885 SimQINCo .713±.137 .946±.015 .889±.043 .644±.079 .923±.020 .951±.013 .794±.026 .919±.030 .994±.003 .920±.085 .912±.094 .919±.091 .877 RQVAE .791±.099 .959±.011 .907±.034 .709±.066 .941±.014 .939±.016 .849±.020 .934±.022 .997±.000 .958±.057 .948±.063 .953±.059 .907 DiVeQ .730±.127 .946±.015 .890±.042 .663±.077 .924±.019 .947±.018 .801±.027 .921±.028 .997±.001 .934±.077 .923±.085 .930±.081 .884 SF-DiVeQ .759±.115 .953±.013 .897±.040 .684±.070 .932±.018 .921±.021 .825±.022 .929±.026 .997±.000 .942±.073 .932±.079 .938±.076 .892 BSQ .629±.147 .877±.030 .838±.058 .594±.081 .851±.035 .871±.038 .685±.032 .866±.046 .965±.015 .844±.094 .833±.109 .841±.106 .808 LFQ .502±.190 .806±.047 .795±.082 .540±.086 .745±.061 .798±.054 .499±.061 .802±.071 .935±.028 .699±.125 .685±.151 .694±.148 .708 f=16f=16 AEKL .615±.167 .889±.027 .826±.061 .571±.092 .851±.034 .901±.027 .666±.038 .878±.046 .974±.006 .850±.113 .837±.128 .846±.125 .809 SoftVQ .612±.176 .912±.024 .849±.059 .587±.090 .878±.032 .910±.029 .650±.048 .889±.046 .989±.009 .864±.115 .842±.132 .854±.128 .820 VQGAN .490±.214 .873±.035 .817±.075 .572±.092 .828±.045 .853±.037 .566±.068 .840±.068 .977±.006 .754±.133 .742±.162 .755±.159 .756 SimVQ .514±.207 .864±.035 .816±.074 .557±.091 .819±.043 .890±.025 .573±.063 .845±.065 .970±.008 .769±.131 .758±.155 .769±.151 .762 SimQINCo .553±.196 .901±.029 .838±.068 .581±.091 .861±.037 .915±.025 .621±.058 .871±.056 .990±.002 .816±.125 .802±.149 .812±.146 .797 RQVAE .647±.160 .926±.022 .862±.055 .603±.089 .892±.030 .933±.017 .709±.041 .901±.042 .997±.000 .885±.109 .868±.122 .878±.119 .842 DiVeQ .551±.197 .899±.029 .835±.068 .583±.092 .856±.039 .907±.028 .612±.058 .868±.057 .990±.002 .817±.126 .802±.148 .812±.145 .794 SF-DiVeQ .549±.198 .898±.029 .834±.068 .581±.092 .859±.038 .900±.022 .621±.058 .868±.058 .990±.002 .813±.125 .800±.150 .810±.146 .793 BSQ .543±.189 .864±.034 .827±.067 .566±.087 .830±.044 .881±.026 .608±.050 .849±.057 .972±.009 .784±.125 .771±.147 .784±.143 .773 LFQ .402±.228 .766±.059 .777±.089 .499±.087 .706±.074 .775±.045 .454±.068 .766±.082 .910±.033 .600±.155 .599±.183 .608±.181 .655 Table S9: Per-dataset LPIPS (↓ ). Cells: mean±σmean_±σ over test images. Method Path Chest Derma OCT Pneu Reti Breast Blood Tiss OrgA OrgC OrgS mean f=4f=4 AEKL .205±.071 .113±.022 .207±.056 .240±.044 .141±.029 .105±.025 .241±.031 .068±.018 .040±.010 .110±.058 .106±.061 .102±.057 .140 SoftVQ .147±.065 .051±.011 .123±.040 .222±.055 .073±.023 .068±.029 .184±.032 .033±.007 .005±.001 .046±.049 .048±.054 .043±.049 .087 VQGAN .076±.043 .017±.004 .051±.018 .096±.027 .029±.009 .014±.006 .082±.015 .013±.003 .001±.000 .013±.022 .013±.024 .011±.018 .035 SimVQ .097±.052 .019±.005 .064±.024 .104±.027 .032±.008 .022±.008 .100±.017 .017±.004 .001±.000 .017±.029 .018±.031 .015±.025 .042 SimQINCo .072±.041 .015±.004 .050±.018 .094±.026 .027±.008 .015±.007 .068±.013 .012±.003 .002±.000 .011±.020 .012±.022 .010±.017 .032 RQVAE .059±.032 .011±.003 .040±.015 .068±.019 .019±.005 .013±.004 .049±.010 .010±.002 .001±.000 .008±.013 .009±.016 .007±.012 .024 DiVeQ .100±.055 .023±.006 .066±.023 .125±.030 .039±.012 .020±.006 .096±.018 .017±.004 .002±.001 .017±.032 .018±.032 .015±.027 .045 SF-DiVeQ .098±.052 .020±.005 .078±.025 .116±.029 .032±.009 .028±.012 .091±.017 .018±.004 .002±.000 .016±.027 .018±.030 .016±.025 .044 BSQ .195±.070 .083±.016 .166±.049 .203±.043 .104±.019 .095±.027 .206±.034 .060±.014 .014±.004 .083±.050 .085±.053 .080±.049 .114 LFQ .211±.081 .088±.016 .179±.058 .157±.035 .110±.019 .118±.028 .210±.035 .061±.022 .019±.006 .092±.049 .093±.061 .090±.057 .119 f=8f=8 AEKL .219±.083 .094±.020 .163±.051 .232±.050 .113±.020 .082±.025 .219±.028 .065±.017 .027±.007 .104±.064 .100±.066 .095±.064 .126 SoftVQ .239±.082 .100±.023 .175±.054 .195±.038 .116±.033 .114±.027 .257±.044 .070±.019 .013±.003 .111±.068 .119±.083 .112±.081 .135 VQGAN .230±.085 .077±.018 .158±.046 .185±.038 .097±.022 .069±.018 .227±.035 .059±.019 .002±.000 .088±.073 .091±.080 .083±.077 .114 SimVQ .174±.083 .049±.010 .100±.032 .145±.029 .073±.017 .038±.015 .170±.028 .035±.010 .003±.001 .055±.056 .054±.056 .049±.052 .079 SimQINCo .199±.091 .056±.012 .115±.035 .184±.041 .078±.019 .048±.014 .204±.031 .041±.012 .003±.000 .061±.065 .062±.065 .057±.062 .092 RQVAE .153±.076 .038±.009 .088±.029 .151±.035 .053±.013 .032±.009 .173±.030 .026±.006 .001±.000 .035±.048 .035±.048 .031±.043 .068 DiVeQ .189±.088 .055±.012 .105±.034 .164±.030 .077±.018 .041±.013 .208±.033 .038±.010 .003±.001 .055±.061 .056±.061 .051±.057 .087 SF-DiVeQ .172±.086 .043±.010 .091±.029 .125±.026 .064±.016 .032±.011 .184±.030 .031±.008 .003±.001 .046±.058 .046±.056 .041±.052 .073 BSQ .269±.086 .118±.024 .210±.057 .179±.031 .139±.026 .137±.033 .255±.037 .087±.023 .031±.008 .136±.063 .140±.076 .135±.074 .153 LFQ .344±.086 .204±.040 .320±.100 .279±.046 .237±.039 .210±.042 .435±.056 .158±.043 .089±.034 .257±.083 .275±.100 .270±.093 .257 f=16f=16 AEKL .241±.090 .099±.021 .160±.048 .240±.046 .122±.022 .082±.021 .244±.033 .074±.023 .028±.008 .122±.078 .121±.083 .114±.080 .137 SoftVQ .227±.092 .073±.017 .132±.047 .214±.047 .089±.020 .068±.021 .243±.038 .060±.024 .007±.002 .110±.078 .109±.083 .103±.080 .120 VQGAN .317±.106 .118±.028 .193±.062 .297±.063 .145±.029 .097±.025 .330±.044 .117±.045 .025±.010 .199±.093 .198±.108 .190±.103 .186 SimVQ .298±.099 .131±.031 .200±.067 .247±.050 .156±.027 .106±.029 .320±.043 .104±.040 .041±.015 .194±.088 .188±.099 .181±.095 .180 SimQINCo .262±.099 .083±.020 .155±.051 .227±.049 .111±.025 .068±.019 .271±.039 .075±.031 .008±.003 .144±.084 .138±.093 .131±.090 .139 RQVAE .223±.096 .060±.014 .124±.045 .179±.036 .083±.018 .050±.014 .206±.034 .055±.022 .002±.000 .091±.076 .091±.078 .084±.076 .104 DiVeQ .266±.101 .090±.022 .154±.052 .241±.048 .116±.024 .082±.020 .274±.036 .083±.032 .008±.004 .146±.082 .142±.092 .135±.089 .145 SF-DiVeQ .263±.096 .086±.021 .147±.050 .217±.045 .110±.023 .066±.019 .270±.038 .079±.031 .009±.004 .150±.085 .144±.095 .137±.092 .140 BSQ .318±.099 .128±.028 .231±.068 .234±.043 .154±.029 .132±.031 .317±.051 .112±.035 .030±.010 .173±.083 .185±.111 .179±.111 .183 LFQ .459±.101 .241±.043 .365±.106 .306±.054 .281±.042 .227±.049 .489±.066 .212±.064 .118±.034 .356±.113 .384±.141 .379±.138 .318 Table S10: Per-dataset pixel-MSE (↓ ). Cells: mean±σmean_±σ over test images. Method Path Chest Derma OCT Pneu Reti Breast Blood Tiss OrgA OrgC OrgS mean f=4f=4 AEKL .0037±.0025 8.1e-4±2.5e-4 .0011±6.4e-4 .0019±7.8e-4 9.1e-4±3.1e-4 8.5e-4±3.7e-4 .0021±5.1e-4 9.4e-4±4.1e-4 1.6e-4±8.1e-5 .0011±7.1e-4 .0012±8.5e-4 .0011±8.2e-4 .0013 SoftVQ .0019±.0013 2.5e-4±1.1e-4 7.4e-4±5.3e-4 .0012±5.8e-4 2.8e-4±1.2e-4 9.0e-4±6.5e-4 9.1e-4±2.8e-4 4.4e-4±1.4e-4 2.3e-5±1.4e-5 3.5e-4±3.7e-4 4.1e-4±4.5e-4 3.7e-4±4.2e-4 6.5e-4 VQGAN .0010±7.7e-4 7.6e-5±2.9e-5 2.2e-4±1.5e-4 6.4e-4±3.4e-4 8.8e-5±3.1e-5 1.2e-4±5.0e-5 2.8e-4±8.5e-5 1.7e-4±6.7e-5 4.2e-6±9.6e-7 8.0e-5±1.2e-4 1.0e-4±2.0e-4 9.3e-5±1.7e-4 2.4e-4 SimVQ .0013±.0011 8.4e-5±3.6e-5 2.4e-4±2.1e-4 7.4e-4±3.9e-4 9.5e-5±4.0e-5 1.7e-4±6.5e-5 3.9e-4±1.3e-4 2.1e-4±8.3e-5 6.5e-6±2.9e-6 1.1e-4±1.7e-4 1.4e-4±2.5e-4 1.3e-4±2.2e-4 3.0e-4 SimQINCo .0010±9.3e-4 6.6e-5±2.4e-5 1.9e-4±1.4e-4 6.4e-4±3.5e-4 8.2e-5±2.9e-5 1.3e-4±5.1e-5 2.8e-4±9.0e-5 1.8e-4±6.6e-5 6.0e-6±3.5e-6 7.3e-5±1.1e-4 9.8e-5±1.9e-4 8.8e-5±1.6e-4 2.4e-4 RQVAE 8.7e-4±7.5e-4 5.2e-5±2.1e-5 1.4e-4±1.1e-4 5.1e-4±2.8e-4 6.0e-5±2.2e-5 1.3e-4±4.5e-5 2.1e-4±6.9e-5 1.6e-4±5.2e-5 3.0e-6±8.1e-7 4.8e-5±7.8e-5 6.7e-5±1.5e-4 6.0e-5±1.2e-4 1.9e-4 DiVeQ .0014±.0012 9.6e-5±4.1e-5 2.3e-4±1.9e-4 8.1e-4±4.2e-4 1.1e-4±4.6e-5 1.3e-4±4.6e-5 4.2e-4±1.3e-4 2.0e-4±8.3e-5 5.6e-6±3.0e-6 1.2e-4±2.0e-4 1.5e-4±2.8e-4 1.3e-4±2.5e-4 3.2e-4 SF-DiVeQ .0014±.0010 9.8e-5±4.0e-5 2.8e-4±2.0e-4 7.8e-4±4.1e-4 1.1e-4±4.9e-5 2.5e-4±1.5e-4 4.4e-4±1.4e-4 2.1e-4±8.3e-5 5.7e-6±2.9e-6 1.2e-4±1.9e-4 1.5e-4±2.7e-4 1.4e-4±2.4e-4 3.3e-4 BSQ .0042±.0027 7.8e-4±4.4e-4 .0013±.0010 .0018±6.8e-4 7.6e-4±3.5e-4 .0012±6.8e-4 .0020±5.8e-4 9.6e-4±4.0e-4 6.7e-5±5.3e-5 .0012±1.0e-3 .0013±.0013 .0012±.0023 .0014 LFQ .0049±.0059 9.2e-4±3.6e-4 .0021±.0018 .0022±8.7e-4 9.6e-4±3.9e-4 .0021±.0013 .0025±7.0e-4 .0010±9.5e-4 1.4e-4±1.6e-4 .0014±7.8e-4 .0015±9.8e-4 .0014±9.3e-4 .0018 f=8f=8 AEKL .0040±.0025 6.8e-4±2.0e-4 9.0e-4±5.7e-4 .0019±7.7e-4 7.7e-4±2.6e-4 7.5e-4±2.5e-4 .0021±5.1e-4 8.6e-4±3.3e-4 1.1e-4±1.6e-4 9.9e-4±7.7e-4 .0011±9.0e-4 .0010±8.6e-4 .0013 SoftVQ .0050±.0032 7.5e-4±3.1e-4 .0010±7.2e-4 .0020±7.4e-4 7.2e-4±2.9e-4 .0013±5.7e-4 .0026±7.6e-4 9.4e-4±4.5e-4 8.8e-5±5.9e-5 .0013±9.9e-4 .0014±.0012 .0013±.0011 .0015 VQGAN .0046±.0033 3.2e-4±1.5e-4 5.4e-4±4.5e-4 .0016±7.1e-4 3.6e-4±1.7e-4 3.4e-4±1.3e-4 .0017±5.9e-4 6.4e-4±3.8e-4 8.4e-6±3.0e-6 7.3e-4±8.5e-4 8.5e-4±.0010 7.6e-4±9.9e-4 .0010 SimVQ .0031±.0023 2.6e-4±9.6e-5 3.9e-4±3.2e-4 .0013±6.2e-4 3.2e-4±1.3e-4 2.6e-4±1.3e-4 .0011±3.4e-4 4.1e-4±2.0e-4 1.5e-5±9.7e-6 4.8e-4±5.7e-4 5.6e-4±6.8e-4 5.0e-4±6.4e-4 7.2e-4 SimQINCo .0033±.0024 2.3e-4±9.9e-5 4.0e-4±3.3e-4 .0014±6.5e-4 2.7e-4±1.2e-4 3.4e-4±1.1e-4 .0012±3.8e-4 4.3e-4±2.4e-4 1.5e-5±4.3e-6 4.7e-4±6.2e-4 5.5e-4±7.3e-4 4.9e-4±7.0e-4 7.6e-4 RQVAE .0024±.0018 1.7e-4±7.4e-5 3.1e-4±2.7e-4 .0011±5.6e-4 2.0e-4±8.8e-5 2.3e-4±6.7e-5 8.8e-4±2.9e-4 3.0e-4±1.4e-4 4.3e-6±1.1e-6 2.8e-4±4.2e-4 3.4e-4±5.2e-4 3.1e-4±4.8e-4 5.5e-4 DiVeQ .0032±.0023 2.4e-4±1.0e-4 4.2e-4±3.4e-4 .0013±6.3e-4 2.7e-4±1.2e-4 2.8e-4±1.1e-4 .0012±4.1e-4 4.3e-4±2.3e-4 9.2e-6±4.9e-6 4.5e-4±6.0e-4 5.3e-4±7.0e-4 4.8e-4±6.7e-4 7.3e-4 SF-DiVeQ .0027±.0020 1.9e-4±8.2e-5 3.4e-4±2.9e-4 .0012±6.0e-4 2.4e-4±1.1e-4 1.9e-4±6.2e-5 9.7e-4±3.0e-4 3.4e-4±1.8e-4 1.3e-5±6.5e-6 3.8e-4±5.2e-4 4.5e-4±6.2e-4 4.1e-4±5.8e-4 6.2e-4 BSQ .0070±.0054 .0013±5.1e-4 .0024±.0014 .0024±8.8e-4 .0015±5.0e-4 .0023±.0013 .0036±.0012 .0018±7.7e-4 2.0e-4±1.6e-4 .0024±.0014 .0025±.0017 .0024±.0016 .0025 LFQ .0123±.0082 .0030±.0016 .0050±.0067 .0039±.0019 .0036±.0016 .0038±.0021 .0108±.0062 .0043±.0020 7.4e-4±.0015 .0070±.0047 .0077±.0053 .0075±.0055 .0058 f=16f=16 AEKL .0049±.0032 6.6e-4±2.2e-4 8.6e-4±5.4e-4 .0019±8.1e-4 7.7e-4±2.8e-4 .0011±3.9e-4 .0023±6.7e-4 9.2e-4±4.6e-4 9.6e-5±4.0e-5 .0011±9.3e-4 .0012±.0011 .0011±.0011 .0014 SoftVQ .0050±.0035 4.2e-4±1.7e-4 6.5e-4±5.6e-4 .0017±7.5e-4 4.8e-4±2.2e-4 5.1e-4±2.1e-4 .0025±8.0e-4 7.3e-4±4.4e-4 4.0e-5±2.3e-5 9.7e-4±9.5e-4 .0011±.0012 .0010±.0011 .0013 VQGAN .0082±.0061 8.2e-4±3.4e-4 9.3e-4±8.3e-4 .0019±7.9e-4 9.7e-4±4.4e-4 .0010±3.6e-4 .0038±.0013 .0015±8.7e-4 9.2e-5±6.7e-5 .0023±.0017 .0026±.0022 .0024±.0022 .0022 SimVQ .0074±.0050 .0010±3.7e-4 .0011±8.3e-4 .0021±8.3e-4 .0012±4.6e-4 .0010±3.0e-4 .0038±.0012 .0015±8.1e-4 1.5e-4±9.7e-5 .0024±.0016 .0025±.0019 .0023±.0019 .0022 SimQINCo .0064±.0047 5.2e-4±2.3e-4 6.3e-4±6.2e-4 .0017±7.7e-4 6.2e-4±2.9e-4 4.1e-4±1.3e-4 .0028±9.6e-4 9.7e-4±6.2e-4 2.9e-5±1.8e-5 .0014±.0012 .0016±.0015 .0014±.0015 .0015 RQVAE .0044±.0031 3.1e-4±1.5e-4 5.0e-4±4.8e-4 .0015±7.3e-4 3.9e-4±1.8e-4 3.3e-4±1.1e-4 .0018±6.2e-4 6.0e-4±3.8e-4 5.9e-6±2.4e-6 7.3e-4±8.5e-4 8.7e-4±.0010 7.8e-4±1.0e-3 .0010 DiVeQ .0065±.0047 5.9e-4±2.4e-4 7.7e-4±7.2e-4 .0017±7.7e-4 7.0e-4±3.2e-4 8.5e-4±1.9e-4 .0030±.0010 .0010±6.4e-4 3.4e-5±2.5e-5 .0015±.0013 .0017±.0016 .0015±.0016 .0017 SF-DiVeQ .0064±.0047 5.4e-4±2.3e-4 6.9e-4±6.4e-4 .0017±7.7e-4 6.5e-4±3.0e-4 4.4e-4±1.4e-4 .0028±9.7e-4 .0010±6.6e-4 4.1e-5±2.9e-5 .0015±.0012 .0016±.0016 .0015±.0015 .0016 BSQ .0080±.0052 .0013±5.2e-4 .0017±.0012 .0027±9.5e-4 .0014±6.7e-4 .0017±9.5e-4 .0042±.0012 .0018±.0010 1.9e-4±1.4e-4 .0029±.0018 .0030±.0022 .0029±.0023 .0027 LFQ .0162±.0112 .0038±.0017 .0050±.0035 .0062±.0027 .0039±.0017 .0043±.0022 .0101±.0036 .0048±.0021 8.2e-4±6.6e-4 .0088±.0045 .0094±.0054 .0088±.0053 .0068 Table S11: Per-dataset reconstruction-FID (↓ ). Dataset-level metric (no per-image variance). Method Path Chest Derma OCT Pneu Reti Breast Blood Tiss OrgA OrgC OrgS mean f=4f=4 AEKL 37.9 23.3 71.3 78.6 47.5 56.9 104 19.2 29.0 45.0 27.6 28.1 47.4 SoftVQ 23.2 7.06 34.2 34.3 20.4 31.7 76.8 10.1 2.52 11.0 6.14 5.65 21.9 VQGAN 11.1 4.53 14.4 15.9 10.8 9.44 33.6 4.79 2.77 1.68 2.24 1.96 9.44 SimVQ 14.7 5.32 16.5 18.3 12.2 12.5 47.1 6.35 1.96 1.51 2.04 1.85 11.7 SimQINCo 11.6 4.03 14.5 18.3 10.1 8.88 33.0 5.17 3.69 1.47 2.02 1.78 9.54 RQVAE 7.29 3.47 12.2 10.5 7.34 10.9 23.8 4.56 0.58 0.85 1.32 1.18 6.99 DiVeQ 16.8 5.93 16.0 24.0 14.2 11.5 49.8 6.35 1.72 1.65 2.16 2.01 12.7 SF-DiVeQ 14.8 5.77 17.3 18.5 14.2 14.6 47.2 7.27 1.90 2.16 2.78 2.52 12.4 BSQ 28.0 11.4 69.0 43.4 29.9 47.7 84.7 18.8 2.51 31.4 17.7 17.1 33.5 LFQ 37.9 15.0 49.6 37.2 42.4 66.8 87.1 17.4 4.48 58.9 31.4 33.7 40.1 f=8f=8 AEKL 41.8 25.1 56.1 86.2 47.5 43.1 136 21.8 15.0 43.3 27.7 27.2 47.5 SoftVQ 42.9 17.9 69.7 101 39.8 57.6 133 20.0 2.12 54.8 32.8 33.0 50.4 VQGAN 35.6 15.6 57.7 93.3 36.1 34.7 125 22.5 1.95 42.6 30.2 28.5 43.7 SimVQ 35.2 6.90 21.9 36.1 23.0 22.3 88.0 13.0 2.75 17.6 11.3 9.98 24.0 SimQINCo 33.3 10.5 32.1 41.1 25.7 24.4 97.2 16.2 2.23 15.4 10.8 10.2 26.6 RQVAE 29.9 7.64 25.2 28.7 20.1 20.5 68.7 11.3 2.11 4.67 4.69 3.98 19.0 DiVeQ 34.3 9.71 28.0 39.9 24.3 24.6 80.7 13.8 5.39 12.3 8.93 8.20 24.2 SF-DiVeQ 38.6 10.0 21.7 35.4 24.0 19.6 87.2 11.9 2.10 8.72 7.15 6.24 22.7 BSQ 49.8 18.9 105 73.9 41.9 75.7 115 23.8 7.98 66.8 37.4 37.9 54.5 LFQ 75.3 70.4 123 109 111 155 155 53.8 55.5 135 99.0 103 104 f=16f=16 AEKL 52.3 32.6 69.3 92.0 56.5 40.6 160 24.9 12.2 53.6 38.0 38.4 55.9 SoftVQ 44.8 19.1 45.4 81.8 42.3 42.4 136 22.8 1.74 57.9 41.4 40.5 48.1 VQGAN 70.6 42.5 86.4 102 68.4 49.5 251 33.9 9.86 95.4 70.6 70.6 79.2 SimVQ 62.9 52.9 88.7 90.9 78.0 48.8 240 31.6 24.2 109 79.1 80.1 82.2 SimQINCo 53.8 30.4 62.7 78.2 56.8 48.5 231 24.8 1.94 77.3 54.8 54.5 64.5 RQVAE 46.1 22.9 32.3 54.8 40.7 35.7 123 19.2 2.83 32.1 25.4 23.6 38.2 DiVeQ 57.8 30.1 62.0 68.6 52.8 43.6 193 25.4 1.83 84.5 59.0 60.5 61.6 SF-DiVeQ 53.2 26.8 60.0 67.8 48.2 40.0 172 23.8 2.70 78.4 55.3 55.7 57.0 BSQ 51.5 30.8 95.4 103 52.6 65.6 154 37.0 9.27 96.9 58.7 60.2 67.9 LFQ 156 117 201 137 143 131 252 86.3 88.1 179 141 145 148 Table S12: Per-dataset reconstruction-FMD (rFMD, ↓ ). Dataset-level metric using each dataset’s own MedMNIST feature extractor; the aggregate is the median over datasets (scales differ per extractor). Method Path Chest Derma OCT Pneu Reti Breast Blood Tiss OrgA OrgC OrgS median f=4f=4 AEKL 17.3 0.829 4.22 2.30 0.770 7.09 59.9 16.8 1.04 0.611 0.581 0.573 1.67 SoftVQ 9.01 0.053 4.26 0.295 0.104 24.8 20.6 6.69 0.165 0.143 0.150 0.147 0.230 VQGAN 2.01 0.005 1.50 0.069 0.021 1.32 1.29 0.606 0.023 0.013 0.010 0.010 0.046 SimVQ 5.62 0.007 1.19 0.116 0.007 1.24 1.19 2.61 0.030 0.058 0.042 0.046 0.087 SimpleQINCo 6.16 0.004 0.528 0.128 0.016 11.8 5.39 2.70 0.024 0.070 0.062 0.068 0.099 RQVAE 2.41 0.004 0.781 0.043 0.012 1.64 0.851 3.22 0.029 0.021 0.018 0.015 0.036 DiVeQ 4.83 0.009 2.14 0.105 0.057 2.07 6.51 2.55 0.036 0.091 0.064 0.062 0.098 SF-DiVeQ 5.45 0.003 1.08 0.036 0.007 5.44 1.96 3.36 0.040 0.008 0.007 0.010 0.038 BSQ 26.2 0.168 8.99 1.05 0.189 22.1 66.2 21.8 0.585 0.470 0.569 0.557 0.819 LFQ 25.9 0.186 11.3 1.29 0.180 107 37.6 21.1 0.449 0.318 0.424 0.593 0.939 f=8f=8 AEKL 18.3 0.447 3.49 2.29 0.230 32.5 56.0 12.4 0.545 0.561 0.295 0.469 1.43 SoftVQ 23.5 0.137 3.85 1.76 0.268 32.9 117 7.27 0.281 0.780 0.428 0.647 1.27 VQGAN 15.7 0.039 7.45 0.547 0.032 4.90 32.8 2.58 0.105 0.177 0.155 0.325 0.436 SimVQ 12.5 0.025 0.538 0.279 0.039 4.30 8.63 2.87 0.029 0.110 0.058 0.103 0.194 SimpleQINCo 14.2 0.025 1.99 0.298 0.074 40.5 23.8 8.78 0.522 0.237 0.155 0.186 0.410 RQVAE 7.45 0.009 0.945 0.121 0.014 4.43 3.30 3.43 0.039 0.041 0.016 0.031 0.081 DiVeQ 7.44 0.015 1.79 0.308 0.016 5.77 8.03 2.54 0.086 0.025 0.030 0.047 0.197 SF-DiVeQ 8.58 0.024 0.842 0.283 0.037 1.76 9.74 2.97 0.064 0.074 0.063 0.099 0.191 BSQ 53.6 1.01 14.7 2.32 0.363 167 111 64.4 2.65 0.685 0.744 1.15 2.48 LFQ 61.5 2.42 17.8 5.43 8.99 152 540 165 7.48 9.44 13.2 13.5 13.4 f=16f=16 AEKL 20.9 0.971 7.05 3.05 0.421 7.20 69.0 15.4 0.611 0.567 0.519 0.833 2.01 SoftVQ 22.2 0.108 4.16 1.37 0.160 29.8 83.4 11.2 0.334 0.493 0.290 0.473 0.933 VQGAN 52.9 0.700 4.04 2.43 0.420 62.4 249 64.1 1.17 1.72 1.59 2.01 2.22 SimVQ 47.3 2.12 4.71 3.61 1.00 12.8 234 39.0 1.13 2.04 1.79 2.09 2.86 SimpleQINCo 31.1 0.192 1.10 0.982 0.180 6.02 103 11.5 0.155 0.747 0.626 0.993 0.988 RQVAE 17.9 0.025 3.17 0.587 0.061 8.37 41.5 9.22 0.028 0.203 0.175 0.291 0.439 DiVeQ 27.1 0.204 5.97 1.49 0.189 52.5 121 11.6 0.060 1.06 0.693 1.18 1.33 SF-DiVeQ 26.1 0.174 3.36 1.53 0.115 1.14 147 13.9 0.177 1.23 0.851 1.13 1.18 BSQ 50.3 0.867 16.0 3.03 0.449 32.9 215 41.0 0.623 1.74 1.70 1.86 2.45 LFQ 62.6 6.16 18.4 9.56 7.89 111 655 115 8.44 15.5 23.5 20.1 19.2 Appendix D Qualitative Reconstructions Figure S8 shows two fixed test subjects (indices 7 and 12) from every MedMNIST dataset, reconstructed by each tokenizer family at the three compression factors. The top row of each panel is the original; the number in the top-right of each cell is that image’s PSNR (dB) against its reference. (a) f=4f=4 (b) f=8f=8 (c) f=16f=16 Figure S8: Qualitative reconstructions of two fixed test subjects per dataset (columns) by every tokenizer family (rows), at compression factors S8 f=4f=4, S8 f=8f=8, and S8 f=16f=16. Top row of each panel is the original; top-right of each cell is per-image PSNR (dB). Reconstruction differences across families grow with compression. Appendix E Quantitative Generation Table S13 gives per-dataset DiT-B/2 generation-FID. The ranking tracks reconstruction closely—consistent with the r=0.82r=0.82 correlation in the main paper—with the soft and space-filling schemes (DiVeQ, SF-DiVeQ) leading at low-to-mid compression and RQVAE retaking the lead at f=16f=16. Table S13: Per-dataset DiT-B/2 generation-FID (↓ ). Dataset-level metric. Method Path Chest Derma OCT Pneu Reti Breast Blood Tiss OrgA OrgC OrgS mean f=4f=4 AEKL 68.4 33.2 100 122 85.1 81.3 137 36.4 41.7 86.8 58.9 63.3 76.2 SoftVQ 111 21.1 102 83.3 101 69.0 155 52.0 13.5 82.9 80.3 88.9 79.9 VQGAN 60.7 18.4 52.8 52.7 68.1 53.7 105 29.4 11.9 42.7 53.3 57.7 50.5 SimVQ 64.3 14.9 77.3 57.3 50.4 51.2 98.3 37.7 9.78 39.2 43.8 48.4 49.4 SimQINCo 75.3 11.2 62.0 51.6 58.8 52.4 108 38.1 8.29 42.6 61.5 58.2 52.3 RQVAE 66.8 14.1 74.9 52.1 76.3 36.2 105 42.4 8.64 44.0 50.9 54.8 52.2 DiVeQ 68.7 23.2 62.3 60.9 95.9 36.3 95.7 34.8 5.07 27.0 32.0 35.2 48.1 SF-DiVeQ 63.0 16.6 70.7 59.0 61.4 46.0 101 43.5 5.12 37.5 36.5 44.2 48.7 BSQ 115 38.6 74.6 89.1 154 76.7 137 89.3 46.1 148 140 146 104 LFQ 133 61.2 131 95.1 167 149 182 126 85.4 241 163 170 142 f=8f=8 AEKL 78.9 38.0 76.9 130 67.0 53.9 163 39.9 24.4 83.5 63.1 68.5 73.9 SoftVQ 85.4 45.7 107 145 133 121 194 89.3 23.8 140 102 108 108 VQGAN 73.1 19.7 76.1 127 65.5 44.1 168 31.0 6.80 69.2 55.6 50.6 65.5 SimVQ 66.9 24.7 57.7 78.7 125 44.2 116 43.6 20.9 74.5 51.9 55.1 63.2 SimQINCo 69.7 19.4 56.2 86.5 61.1 53.7 126 26.1 5.01 45.4 40.3 44.7 52.8 RQVAE 60.2 17.9 91.2 68.8 80.8 59.7 112 34.3 7.98 41.3 45.6 46.1 55.5 DiVeQ 90.5 21.4 79.6 81.5 59.0 41.1 120 41.6 15.8 52.5 46.3 51.6 58.4 SF-DiVeQ 74.8 27.6 64.4 91.1 112 49.4 110 29.9 14.5 44.8 45.1 43.4 58.8 BSQ 93.6 33.5 94.3 112 60.2 76.9 135 78.6 15.1 102 88.1 88.0 81.5 LFQ 189 181 259 256 272 181 318 226 126 257 218 230 226 f=16f=16 AEKL 78.7 42.9 95.9 126 89.0 66.6 218 47.2 12.1 113 81.2 95.5 88.8 SoftVQ 88.7 39.0 108 118 127 107 220 102 20.5 158 137 140 114 VQGAN 91.0 53.0 122 148 85.7 53.4 298 37.9 14.7 110 93.3 87.8 99.5 SimVQ 92.1 69.9 141 120 121 58.2 274 58.2 37.7 139 113 116 112 SimQINCo 68.1 38.7 113 120 85.5 68.8 285 42.4 4.56 111 76.8 84.1 91.5 RQVAE 73.0 32.9 71.0 101 66.4 63.9 182 52.6 13.1 65.0 61.5 63.3 70.5 DiVeQ 75.6 37.1 78.5 109 68.6 60.7 257 40.3 4.79 142 116 105 91.2 SF-DiVeQ 74.1 34.1 83.5 112 70.7 60.0 206 36.9 4.99 124 100 99.0 83.7 BSQ 107 41.0 106 138 73.7 58.1 213 73.6 13.5 145 133 129 102 LFQ 154 103 181 108 113 121 298 59.9 74.9 166 144 138 138 Table S14: Per-dataset DiT-B/2 generation-FMD (gFMD, ↓ ). Dataset-level metric using each dataset’s own MedMNIST feature extractor; the aggregate is the median over datasets. Method Path Chest Derma OCT Pneu Reti Breast Blood Tiss OrgA OrgC OrgS median f=4f=4 AEKL 98.3 1.63 18.0 4.70 28.2 49.8 450 62.7 8.18 20.6 21.7 23.0 22.4 SoftVQ 43.7 2.07 63.8 3.07 11.9 35.5 37.9 87.1 17.1 12.2 18.9 21.5 20.2 VQGAN 38.2 4.13 26.2 3.15 41.2 210 234 61.5 10.4 25.9 26.5 20.0 26.4 SimVQ 41.5 3.35 15.4 4.18 7.59 83.6 45.1 51.5 8.51 9.24 14.5 24.0 14.9 SimpleQINCo 55.1 0.799 21.4 5.62 6.24 80.8 322 34.6 10.2 29.7 26.3 38.1 28.0 RQVAE 32.0 1.45 33.9 2.89 16.8 67.7 6.56 82.1 9.85 23.0 28.8 52.7 25.9 DiVeQ 35.9 1.91 7.44 3.28 55.8 29.8 79.1 85.6 4.53 5.55 10.9 12.1 11.5 SF-DiVeQ 28.5 4.33 67.8 5.14 45.4 39.4 46.3 73.4 4.61 16.4 14.2 23.7 26.1 BSQ 37.1 13.6 20.7 13.7 111 78.3 15.6 90.3 27.8 34.2 62.3 87.3 35.6 LFQ 69.1 5.66 64.6 3.32 47.0 126 217 221 32.1 51.2 50.2 60.8 56.0 f=8f=8 AEKL 56.1 2.10 11.6 8.98 24.8 18.9 159 34.6 5.93 29.7 12.0 18.1 18.5 SoftVQ 54.4 3.15 60.4 6.07 50.2 586 522 72.1 16.0 20.5 27.6 25.5 38.9 VQGAN 104 0.529 18.3 6.43 20.0 54.1 208 17.7 9.27 7.92 12.6 21.9 18.0 SimVQ 46.1 7.44 34.5 4.09 70.7 35.4 185 36.9 14.9 18.9 14.8 28.5 31.5 SimpleQINCo 79.5 0.564 25.9 5.54 15.1 50.6 54.9 39.4 6.25 17.2 13.5 21.2 19.2 RQVAE 31.6 5.54 40.9 2.77 6.45 58.7 76.7 26.6 4.79 7.33 9.80 10.3 10.0 DiVeQ 56.5 1.40 7.60 3.11 2.73 221 144 21.6 7.56 13.5 13.0 27.3 13.2 SF-DiVeQ 64.5 4.11 85.3 3.91 49.8 22.1 89.2 43.2 8.96 10.4 12.0 11.4 17.1 BSQ 81.5 1.74 15.6 9.15 12.2 335 199 66.4 20.2 19.9 34.0 32.5 26.4 LFQ 54.9 4.24 24.3 4.46 19.4 453 555 165 27.2 32.9 44.4 68.1 38.7 f=16f=16 AEKL 232 1.56 52.6 12.7 69.2 19.6 226 56.8 8.09 13.5 14.3 22.4 21.0 SoftVQ 53.6 3.51 27.9 5.83 2.81 45.7 49.0 24.6 11.9 6.48 8.08 8.39 10.1 VQGAN 73.9 2.78 6.38 16.2 25.4 77.8 405 109 9.82 13.8 9.84 11.8 15.0 SimVQ 86.7 1.63 11.9 13.0 75.9 163 467 127 10.7 38.0 30.1 18.5 34.0 SimpleQINCo 168 0.875 78.4 3.95 76.1 43.2 385 45.4 5.06 23.2 12.8 20.6 33.2 RQVAE 130 1.00 17.5 6.00 44.7 133 276 58.4 5.96 13.8 8.76 11.3 15.7 DiVeQ 206 1.02 13.5 5.86 23.7 104 428 25.7 2.90 25.4 16.7 18.6 21.2 SF-DiVeQ 74.4 0.602 10.8 8.98 3.67 38.9 323 43.5 3.13 11.7 7.73 13.9 11.2 BSQ 98.2 4.61 58.8 7.34 5.07 126 195 62.7 10.2 11.2 20.8 21.6 21.2 LFQ 72.6 6.88 36.5 10.1 34.1 66.2 670 142 11.1 19.1 29.7 24.7 31.9 Appendix F Qualitative Generations Figure S9 shows two conditional DiT samples per dataset from every tokenizer family at each compression factor, complementing the quantitative gFID results with a visual sense of how sample quality and diversity degrade as the bottleneck tightens. (a) f=4f=4 (b) f=8f=8 (c) f=16f=16 Figure S9: Qualitative generations of two unconditional DiT samples per dataset (columns) by every tokenizer family (rows), at compression factors S9 f=4f=4, S9 f=8f=8, and S9 f=16f=16. Sample quality and diversity degrade with compression. Appendix G Codebook Statistics We characterise the discrete bottleneck by Usage (Tab. S15), the fraction of codes ever selected; normalised Entropy (Tab. S16), H()/log2KH(C)/ _2K of the empirical code distribution; and Utility (Tab. S17), 1/(1+CV)1/(1+CV) with CV=σ(p)/μ(p)CV=σ(p)/μ(p). Continuous baselines have no codebook and are omitted. Usage saturates near 100%100\% for most modern schemes yet collapses for VQGAN as f grows—motivating the latent-geometry analysis, since high usage does not imply an efficiently used latent. Table S15: Per-dataset codebook Usage (↑ ). Method Path Chest Derma OCT Pneu Reti Breast Blood Tiss OrgA OrgC OrgS mean f=4f=4 VQGAN 0.79 0.79 0.79 0.79 0.78 0.73 0.78 0.74 0.31 0.79 0.79 0.79 0.74 SimVQ 1.00 1.00 0.95 0.98 0.98 0.87 0.96 0.95 0.57 1.00 1.00 1.00 0.94 SimQINCo 1.00 1.00 0.99 0.98 0.97 0.82 0.97 0.93 0.37 1.00 1.00 1.00 0.92 RQVAE 0.99 1.00 0.96 0.99 0.97 0.92 0.97 0.92 0.60 1.00 1.00 1.00 0.94 DiVeQ 1.00 1.00 0.99 1.00 0.99 0.96 0.99 0.96 0.83 1.00 1.00 1.00 0.98 SF-DiVeQ 0.32 0.33 0.31 0.31 0.31 0.31 0.30 0.30 0.31 0.32 0.32 0.32 0.31 BSQ 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 LFQ 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 f=8f=8 VQGAN 0.12 0.12 0.11 0.12 0.12 0.11 0.12 0.12 0.11 0.12 0.12 0.12 0.11 SimVQ 1.00 1.00 0.86 0.94 0.88 0.60 0.77 0.93 0.97 1.00 1.00 1.00 0.91 SimQINCo 1.00 1.00 0.92 0.93 0.93 0.77 0.92 0.98 0.84 1.00 1.00 1.00 0.94 RQVAE 0.97 1.00 0.88 0.96 0.91 0.63 0.89 0.95 0.70 1.00 1.00 1.00 0.91 DiVeQ 1.00 1.00 0.94 0.98 0.96 0.80 0.94 0.99 1.00 1.00 1.00 1.00 0.97 SF-DiVeQ 1.00 1.00 1.00 1.00 1.00 0.98 0.99 1.00 1.00 1.00 1.00 1.00 1.00 BSQ 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 LFQ 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 f=16f=16 VQGAN 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 SimVQ 0.98 0.99 0.65 0.44 0.56 0.33 0.29 0.93 0.98 1.00 1.00 1.00 0.76 SimQINCo 1.00 0.99 0.79 0.77 0.81 0.57 0.70 0.95 0.93 1.00 1.00 1.00 0.88 RQVAE 0.97 0.98 0.77 0.76 0.78 0.47 0.69 0.94 0.92 0.98 0.98 0.97 0.85 DiVeQ 1.00 1.00 0.95 0.95 0.89 0.87 0.78 1.00 1.00 1.00 1.00 1.00 0.95 SF-DiVeQ 0.62 0.62 0.59 0.59 0.58 0.49 0.52 0.61 0.63 0.63 0.62 0.62 0.59 BSQ 0.98 1.00 0.65 0.49 0.34 0.16 0.11 0.81 1.00 1.00 0.99 0.99 0.71 LFQ 0.47 0.45 0.30 0.35 0.20 0.08 0.09 0.34 0.78 0.57 0.52 0.53 0.39 Table S16: Per-dataset codebook Entropy (↑ ). Method Path Chest Derma OCT Pneu Reti Breast Blood Tiss OrgA OrgC OrgS mean f=4f=4 VQGAN 0.95 0.90 0.88 0.92 0.90 0.85 0.93 0.83 0.71 0.88 0.88 0.88 0.88 SimVQ 0.95 0.93 0.89 0.92 0.92 0.86 0.94 0.87 0.75 0.93 0.93 0.93 0.90 SimQINCo 0.97 0.93 0.90 0.94 0.94 0.85 0.96 0.86 0.69 0.91 0.91 0.91 0.90 RQVAE 0.71 0.69 0.69 0.71 0.70 0.69 0.71 0.68 0.63 0.69 0.69 0.69 0.69 DiVeQ 0.95 0.93 0.91 0.96 0.93 0.86 0.97 0.89 0.86 0.93 0.93 0.93 0.92 SF-DiVeQ 0.83 0.83 0.77 0.83 0.82 0.80 0.85 0.77 0.81 0.82 0.83 0.83 0.82 BSQ 1.00 1.00 0.99 0.99 1.00 0.99 1.00 0.99 0.99 0.99 0.99 0.99 0.99 LFQ 1.00 0.99 0.99 0.99 0.99 0.99 1.00 0.99 0.99 1.00 1.00 1.00 0.99 f=8f=8 VQGAN 0.74 0.74 0.69 0.71 0.74 0.67 0.75 0.70 0.66 0.76 0.76 0.76 0.72 SimVQ 0.86 0.78 0.75 0.86 0.77 0.78 0.87 0.78 0.69 0.82 0.81 0.81 0.80 SimQINCo 0.97 0.96 0.91 0.93 0.95 0.88 0.96 0.92 0.85 0.97 0.97 0.97 0.94 RQVAE 0.77 0.75 0.74 0.76 0.75 0.73 0.76 0.74 0.68 0.75 0.76 0.75 0.74 DiVeQ 0.97 0.96 0.92 0.95 0.95 0.90 0.97 0.93 0.94 0.97 0.97 0.97 0.95 SF-DiVeQ 0.99 0.98 0.97 0.99 0.98 0.95 0.98 0.96 0.93 0.98 0.98 0.98 0.97 BSQ 1.00 1.00 0.99 0.99 0.99 0.97 0.99 0.99 1.00 1.00 1.00 1.00 0.99 LFQ 1.00 0.99 0.99 0.99 0.99 0.97 0.99 0.99 1.00 1.00 1.00 1.00 0.99 f=16f=16 VQGAN 0.53 0.51 0.48 0.48 0.51 0.48 0.53 0.51 0.48 0.54 0.54 0.54 0.51 SimVQ 0.68 0.54 0.51 0.45 0.54 0.49 0.58 0.64 0.43 0.62 0.62 0.62 0.56 SimQINCo 0.98 0.95 0.90 0.91 0.94 0.88 0.94 0.94 0.91 0.98 0.98 0.98 0.94 RQVAE 0.87 0.84 0.82 0.82 0.84 0.81 0.85 0.84 0.81 0.87 0.86 0.86 0.84 DiVeQ 0.98 0.97 0.95 0.95 0.96 0.95 0.96 0.96 0.97 0.98 0.98 0.98 0.96 SF-DiVeQ 0.93 0.92 0.89 0.90 0.92 0.86 0.91 0.90 0.90 0.93 0.93 0.93 0.91 BSQ 0.98 0.99 0.94 0.93 0.90 0.80 0.82 0.96 0.99 0.99 0.99 0.99 0.94 LFQ 0.90 0.85 0.85 0.89 0.85 0.71 0.79 0.84 0.91 0.91 0.90 0.91 0.86 Table S17: Per-dataset codebook Utility (↑ ). Method Path Chest Derma OCT Pneu Reti Breast Blood Tiss OrgA OrgC OrgS mean f=4f=4 VQGAN 0.49 0.38 0.36 0.40 0.40 0.25 0.47 0.24 0.19 0.30 0.31 0.31 0.34 SimVQ 0.47 0.42 0.37 0.40 0.41 0.28 0.45 0.29 0.21 0.37 0.40 0.40 0.37 SimQINCo 0.57 0.45 0.40 0.44 0.48 0.26 0.55 0.27 0.18 0.33 0.35 0.35 0.39 RQVAE 0.11 0.10 0.10 0.11 0.11 0.11 0.11 0.10 0.09 0.10 0.10 0.10 0.10 DiVeQ 0.50 0.44 0.39 0.53 0.42 0.27 0.56 0.37 0.34 0.41 0.44 0.43 0.43 SF-DiVeQ 0.32 0.31 0.25 0.31 0.30 0.25 0.35 0.20 0.27 0.28 0.30 0.30 0.29 BSQ 0.81 0.77 0.72 0.77 0.79 0.68 0.80 0.75 0.73 0.79 0.73 0.71 0.75 LFQ 0.80 0.74 0.75 0.76 0.75 0.67 0.82 0.71 0.78 0.81 0.81 0.81 0.77 f=8f=8 VQGAN 0.21 0.21 0.15 0.17 0.20 0.14 0.23 0.15 0.14 0.23 0.23 0.23 0.19 SimVQ 0.18 0.08 0.09 0.18 0.08 0.15 0.20 0.09 0.05 0.09 0.09 0.09 0.11 SimQINCo 0.55 0.50 0.39 0.41 0.48 0.30 0.53 0.36 0.28 0.52 0.53 0.52 0.45 RQVAE 0.13 0.12 0.13 0.13 0.12 0.14 0.13 0.12 0.10 0.12 0.12 0.12 0.12 DiVeQ 0.57 0.51 0.41 0.48 0.49 0.30 0.56 0.36 0.44 0.52 0.55 0.55 0.48 SF-DiVeQ 0.74 0.61 0.53 0.70 0.61 0.48 0.64 0.47 0.40 0.56 0.56 0.55 0.57 BSQ 0.82 0.78 0.71 0.75 0.75 0.51 0.69 0.71 0.81 0.84 0.82 0.81 0.75 LFQ 0.79 0.68 0.70 0.70 0.69 0.51 0.66 0.66 0.78 0.79 0.77 0.76 0.71 f=16f=16 VQGAN 0.09 0.08 0.06 0.06 0.08 0.06 0.09 0.07 0.06 0.09 0.09 0.09 0.08 SimVQ 0.04 0.02 0.02 0.02 0.03 0.02 0.03 0.03 0.02 0.03 0.03 0.03 0.03 SimQINCo 0.62 0.49 0.36 0.38 0.47 0.34 0.50 0.41 0.39 0.65 0.61 0.61 0.49 RQVAE 0.27 0.23 0.24 0.22 0.23 0.24 0.25 0.23 0.20 0.26 0.25 0.25 0.24 DiVeQ 0.59 0.54 0.48 0.50 0.51 0.42 0.53 0.47 0.56 0.61 0.60 0.61 0.54 SF-DiVeQ 0.48 0.45 0.38 0.39 0.44 0.30 0.43 0.37 0.37 0.47 0.47 0.47 0.42 BSQ 0.61 0.60 0.42 0.43 0.37 0.15 0.25 0.46 0.72 0.67 0.63 0.63 0.50 LFQ 0.32 0.18 0.22 0.30 0.25 0.09 0.19 0.18 0.31 0.31 0.32 0.32 0.25 Appendix H Linear Probing We fit a linear classifier on the frozen pre-quantization latent ez_e (Tab. S18) and repeat it on the post-quantization latent zqz_q (Tab. S19), each under the per-dataset task-appropriate primary metric (top-1 accuracy for multi-class; macro-AUROC for multi-label ChestMNIST; quadratic-weighted κ for ordinal RetinaMNIST). The near-identical means between zez_e and zqz_q confirm that discretization is largely information-preserving, except for the lookup-free families (LFQ, BSQ); the continuous AEKL and SoftVQ autoencoders have no discrete bottleneck and are omitted from Tab. S19. Table S18: Per-dataset linear-probing primary metric (↑ , on zez_e). Method Path Chest Derma OCT Pneu Reti Breast Blood Tiss OrgA OrgC OrgS mean f=4f=4 AEKL .789 .584 .682 .721 .979 .581 .774 .934 .686 .989 .984 .934 .803 SoftVQ .921 .610 .781 .828 .989 .587 .863 .974 .780 .996 .993 .979 .858 VQGAN .865 .609 .775 .820 .984 .606 .880 .961 .807 .990 .987 .963 .854 SimVQ .799 .603 .718 .786 .984 .596 .848 .963 .802 .989 .983 .955 .836 SimQINCo .858 .606 .782 .791 .986 .608 .867 .961 .803 .988 .985 .961 .850 RQVAE .865 .597 .755 .780 .985 .635 .845 .963 .788 .991 .985 .968 .847 DiVeQ .856 .608 .737 .794 .987 .638 .867 .969 .802 .992 .987 .965 .850 SF-DiVeQ .847 .603 .703 .787 .983 .526 .871 .959 .806 .991 .986 .966 .836 BSQ .911 .599 .728 .853 .985 .516 .868 .967 .764 .995 .993 .971 .846 LFQ .902 .573 .682 .840 .988 .651 .819 .961 .752 .997 .995 .973 .844 f=8f=8 AEKL .854 .612 .688 .776 .978 .614 .723 .933 .764 .988 .976 .949 .821 SoftVQ .938 .649 .776 .849 .978 .621 .695 .968 .815 .995 .993 .977 .854 VQGAN .896 .656 .770 .801 .983 .596 .881 .946 .799 .990 .982 .956 .855 SimVQ .835 .633 .764 .835 .984 .652 .831 .967 .801 .993 .988 .967 .854 SimQINCo .880 .639 .761 .823 .983 .667 .851 .954 .800 .988 .979 .954 .857 RQVAE .875 .626 .734 .782 .978 .615 .859 .952 .802 .993 .991 .964 .848 DiVeQ .856 .640 .715 .829 .982 .580 .847 .963 .795 .994 .988 .971 .847 SF-DiVeQ .906 .642 .785 .849 .988 .653 .904 .977 .811 .997 .994 .978 .874 BSQ .874 .622 .710 .837 .986 .596 .799 .939 .793 .993 .994 .968 .843 LFQ .887 .616 .709 .803 .981 .632 .851 .935 .781 .992 .991 .969 .846 f=16f=16 AEKL .877 .643 .750 .796 .973 .669 .836 .939 .762 .987 .982 .948 .847 SoftVQ .921 .663 .816 .876 .979 .662 .778 .975 .806 .997 .994 .979 .870 VQGAN .904 .678 .778 .834 .983 .661 .876 .955 .781 .986 .977 .946 .863 SimVQ .896 .664 .816 .860 .990 .636 .917 .961 .797 .992 .989 .966 .874 SimQINCo .901 .672 .792 .812 .982 .639 .895 .959 .775 .990 .979 .954 .862 RQVAE .902 .657 .790 .805 .982 .625 .851 .957 .780 .990 .987 .966 .858 DiVeQ .927 .673 .778 .800 .987 .658 .822 .958 .782 .990 .983 .964 .860 SF-DiVeQ .913 .679 .804 .840 .989 .638 .819 .968 .800 .993 .990 .971 .867 BSQ .925 .659 .756 .876 .989 .572 .779 .954 .830 .994 .994 .970 .858 LFQ .877 .657 .745 .817 .980 .654 .855 .959 .826 .998 .997 .982 .862 Table S19: Per-dataset linear-probing primary metric (↑ , on zqz_q). Method Path Chest Derma OCT Pneu Reti Breast Blood Tiss OrgA OrgC OrgS mean f=4f=4 AEKL – – – – – – – – – – – – – SoftVQ – – – – – – – – – – – – – VQGAN .864 .607 .775 .820 .984 .610 .882 .960 .804 .990 .987 .963 .854 SimVQ .797 .603 .718 .785 .984 .596 .850 .963 .800 .989 .983 .955 .835 SimQINCo .858 .605 .785 .791 .986 .609 .865 .961 .800 .988 .985 .960 .849 RQVAE .865 .598 .755 .780 .985 .635 .845 .963 .788 .991 .985 .968 .847 DiVeQ .856 .608 .738 .794 .987 .663 .866 .969 .802 .992 .987 .965 .852 SF-DiVeQ .846 .603 .705 .785 .983 .534 .870 .959 .805 .991 .986 .966 .836 BSQ .875 .595 .700 .793 .952 .497 .815 .935 .747 .988 .982 .949 .819 LFQ .851 .571 .660 .821 .985 .571 .792 .950 .745 .995 .990 .966 .825 f=8f=8 AEKL – – – – – – – – – – – – – SoftVQ – – – – – – – – – – – – – VQGAN .891 .656 .769 .799 .983 .581 .883 .946 .798 .990 .982 .956 .853 SimVQ .835 .632 .764 .831 .983 .664 .820 .966 .799 .993 .988 .966 .853 SimQINCo .878 .639 .759 .821 .983 .672 .852 .953 .798 .988 .979 .954 .856 RQVAE .875 .626 .735 .782 .978 .615 .858 .952 .802 .993 .991 .964 .848 DiVeQ .858 .640 .713 .828 .982 .543 .843 .962 .793 .994 .988 .971 .843 SF-DiVeQ .906 .643 .782 .847 .988 .648 .896 .977 .808 .997 .994 .978 .872 BSQ .839 .604 .690 .757 .985 .628 .784 .936 .748 .991 .991 .965 .827 LFQ .850 .611 .683 .772 .978 .615 .851 .920 .760 .989 .987 .959 .831 f=16f=16 AEKL – – – – – – – – – – – – – SoftVQ – – – – – – – – – – – – – VQGAN .889 .675 .772 .823 .982 .680 .875 .954 .776 .986 .977 .946 .861 SimVQ .890 .660 .807 .839 .990 .584 .914 .957 .788 .992 .988 .964 .864 SimQINCo .898 .670 .792 .808 .983 .647 .901 .958 .773 .990 .978 .955 .863 RQVAE .902 .657 .790 .804 .982 .623 .849 .957 .779 .990 .987 .966 .857 DiVeQ .926 .671 .774 .797 .986 .664 .827 .958 .781 .990 .983 .964 .860 SF-DiVeQ .912 .678 .807 .838 .989 .625 .830 .967 .798 .993 .990 .971 .866 BSQ .882 .623 .722 .788 .989 .665 .811 .948 .789 .994 .993 .972 .848 LFQ .832 .660 .724 .765 .978 .569 .806 .937 .804 .994 .992 .971 .836 Table S20: Downstream probing gap Δ=M(ze)−M(zq) =M(z_e)-M(z_q) (Sec. 4.7), mean±σmean_±σ over the twelve datasets (each under its primary metric), per compression factor. Larger Δ means discretization erodes more class-discriminative structure; bold marks the smallest gap per column. Method f=4f=4 f=8f=8 f=16f=16 VQGAN [43] 0.000±0.009 0.008±0.025 0.001±0.014 SimVQ [34] -0.002±0.006 0.001±0.017 0.008±0.006 SimQINCo [54] 0.002±0.006 -0.001±0.006 -0.001±0.010 RQVAE [55] 0.000±0.000 0.000±0.000 -0.001±0.006 DiVeQ [49] 0.001±0.006 -0.002±0.011 -0.003±0.009 SF-DiVeQ [49] -0.001±0.005 0.003±0.009 -0.004±0.017 BSQ [53] 0.046±0.033 0.021±0.013 0.018±0.029 LFQ [52] 0.031±0.029 0.027±0.021 0.037±0.024 Appendix I Memorization We test training-set replication with a nearest-neighbour copy detector under two feature spaces: SSCD, purpose-built for copy detection (Tabs. S22 and S23), and DINOv2, which captures higher-level semantic similarity and validates the SSCD analysis in a richer space (Tabs. S24 and S25). Copy-rates are near zero almost everywhere, concentrating only in the lowest-variance modalities (OCT, Path); Fig. S10 shows this is driven by the dataset, not the quantizer. Figure S10: Memorization concentrates by dataset, not architecture. Per-(family, dataset) copy-rate at f=8f=8 under SSCD (left) and DINOv2 (right) features; rows are quantizer families, columns datasets. Elevated values cluster in the lowest-variance modalities (OCT, Path) and are largely constant across families, indicating the dataset regime governs replication. Figure S11: Memorization is not a generator-underfitting artifact. Copy-rate and N-distance ratio vs. gFID (SSCD, DINOv2), colored by family. Copy-rate is decoupled from gFID (r=−0.05/−0.15r=-0.05/-0.15) and elevated copies come from the best (low-gFID) generators; N-distance ratios stay near one throughout. Table S21: Per-dataset variance/diversity of the reference images (grayscale, up to 1,200 samples each), sorted from least to most diverse by effective rank. Eff. rank: effective number of PCA directions (trace/λmax/ _ of the sample Gram matrix); N sim: mean nearest-neighbour cosine similarity (higher == more near-duplicates); Pairwise dist: mean pairwise cosine distance (lower == more homogeneous). Dataset Pixel std ↓ Eff. rank ↓ N sim ↑ Pairwise dist ↓ Reti 0.214 1.7 0.986 0.086 Path 0.194 2.3 0.976 0.047 Derma 0.146 2.5 0.993 0.029 OrgS 0.267 2.8 0.938 0.215 OCT 0.233 3.0 0.909 0.421 OrgA 0.278 3.0 0.945 0.251 Pneu 0.178 3.5 0.984 0.044 OrgC 0.262 3.4 0.934 0.216 Chest 0.247 3.6 0.974 0.092 Breast 0.218 3.6 0.922 0.164 Tiss 0.100 3.8 0.891 0.285 Blood 0.191 3.9 0.987 0.033 Table S22: Per-dataset copy rate (↓ ), SSCD features. Method Path Chest Derma OCT Pneu Reti Breast Blood Tiss OrgA OrgC OrgS mean f=4f=4 AEKL .084 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .007 SoftVQ .128 .005 .000 .017 .000 .000 .000 .000 .001 .000 .000 .000 .013 VQGAN .017 .003 .000 .048 .000 .000 .000 .000 .001 .000 .000 .000 .006 SimVQ .060 .001 .000 .032 .000 .000 .000 .000 .005 .000 .000 .000 .008 SimQINCo .045 .001 .000 .003 .000 .000 .000 .000 .000 .000 .000 .001 .004 RQVAE .031 .007 .000 .124 .000 .000 .000 .000 .013 .000 .000 .000 .015 DiVeQ .047 .005 .000 .037 .000 .000 .000 .000 .011 .003 .000 .004 .009 SF-DiVeQ .020 .000 .000 .000 .000 .000 .000 .000 .002 .000 .000 .001 .002 BSQ .008 .000 .000 .015 .000 .000 .000 .000 .000 .000 .000 .000 .002 LFQ .003 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 f=8f=8 AEKL .054 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .005 SoftVQ .010 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .001 VQGAN .064 .002 .000 .000 .000 .000 .000 .000 .007 .001 .000 .001 .006 SimVQ .036 .000 .000 .000 .000 .000 .000 .000 .003 .000 .000 .001 .003 SimQINCo .082 .000 .000 .000 .000 .000 .000 .000 .001 .001 .000 .001 .007 RQVAE .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 DiVeQ .144 .001 .000 .000 .000 .000 .000 .000 .003 .003 .000 .004 .013 SF-DiVeQ .081 .000 .000 .004 .000 .000 .000 .000 .006 .000 .000 .003 .008 BSQ .039 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .003 LFQ .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 f=16f=16 AEKL .112 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .009 SoftVQ .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 VQGAN .011 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .001 SimVQ .038 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .003 SimQINCo .037 .000 .000 .000 .000 .000 .000 .000 .003 .000 .000 .000 .003 RQVAE .029 .000 .000 .002 .000 .000 .000 .000 .009 .002 .001 .001 .004 DiVeQ .056 .000 .000 .000 .000 .000 .000 .000 .002 .000 .000 .000 .005 SF-DiVeQ .023 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .002 BSQ .112 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .009 LFQ .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 Table S23: Per-dataset memorization ratio (↑ ), SSCD features. Method Path Chest Derma OCT Pneu Reti Breast Blood Tiss OrgA OrgC OrgS mean f=4f=4 AEKL .898 .911 .861 .911 .904 .857 .900 .896 .922 .930 .913 .916 .902 SoftVQ .900 .907 .891 .883 .904 .861 .898 .885 .918 .918 .904 .907 .898 VQGAN .898 .896 .867 .865 .885 .846 .887 .884 .914 .917 .905 .906 .889 SimVQ .900 .904 .878 .881 .897 .852 .883 .890 .910 .914 .896 .901 .892 SimQINCo .900 .900 .871 .884 .885 .840 .880 .883 .917 .915 .896 .899 .889 RQVAE .900 .896 .879 .859 .887 .853 .872 .889 .907 .914 .895 .896 .887 DiVeQ .895 .890 .874 .872 .886 .838 .876 .883 .906 .906 .891 .893 .884 SF-DiVeQ .899 .907 .865 .888 .899 .844 .887 .884 .911 .920 .903 .905 .893 BSQ .906 .909 .883 .892 .913 .862 .912 .902 .920 .933 .910 .915 .905 LFQ .913 .928 .902 .922 .928 .902 .930 .921 .945 .950 .936 .936 .926 f=8f=8 AEKL .896 .905 .866 .907 .896 .843 .899 .888 .913 .921 .902 .906 .895 SoftVQ .912 .908 .875 .904 .901 .861 .913 .900 .914 .930 .916 .918 .904 VQGAN .900 .896 .867 .892 .889 .843 .902 .887 .906 .906 .892 .889 .889 SimVQ .903 .903 .874 .888 .900 .843 .889 .890 .907 .910 .886 .887 .890 SimQINCo .900 .904 .865 .887 .891 .835 .893 .886 .913 .905 .885 .887 .888 RQVAE .942 .960 .950 .967 .881 .958 .950 .963 .974 .963 .955 .946 .951 DiVeQ .893 .899 .868 .890 .891 .846 .889 .883 .909 .898 .880 .883 .886 SF-DiVeQ .896 .909 .875 .884 .902 .842 .897 .886 .904 .908 .893 .895 .891 BSQ .903 .912 .870 .908 .900 .858 .909 .902 .930 .936 .922 .922 .906 LFQ .931 .950 .917 .940 .938 .925 .941 .934 .947 .955 .946 .947 .939 f=16f=16 AEKL .903 .900 .878 .905 .894 .837 .896 .900 .913 .920 .909 .911 .897 SoftVQ .962 .967 .951 .962 .942 .947 .922 .965 .959 .961 .954 .953 .954 VQGAN .910 .901 .877 .913 .892 .839 .913 .909 .923 .930 .917 .919 .904 SimVQ .906 .902 .869 .905 .888 .843 .914 .907 .920 .935 .920 .924 .903 SimQINCo .907 .900 .879 .903 .889 .846 .908 .899 .909 .927 .911 .914 .899 RQVAE .899 .906 .871 .891 .895 .837 .902 .894 .906 .901 .893 .895 .891 DiVeQ .904 .901 .873 .901 .895 .840 .909 .900 .908 .923 .910 .909 .898 SF-DiVeQ .904 .902 .868 .899 .891 .836 .901 .899 .912 .926 .911 .914 .897 BSQ .899 .909 .880 .909 .901 .855 .909 .905 .916 .932 .921 .922 .905 LFQ .919 .910 .871 .917 .900 .873 .929 .911 .929 .944 .933 .933 .914 Table S24: Per-dataset copy rate (↓ ), DINOv2 features. Method Path Chest Derma OCT Pneu Reti Breast Blood Tiss OrgA OrgC OrgS mean f=4f=4 AEKL .022 .000 .000 .004 .000 .000 .000 .000 .003 .000 .002 .004 .003 SoftVQ .069 .000 .000 .030 .000 .000 .000 .000 .022 .000 .002 .003 .010 VQGAN .037 .003 .000 .159 .000 .000 .000 .000 .010 .001 .004 .005 .018 SimVQ .085 .001 .000 .213 .000 .000 .000 .000 .035 .001 .007 .013 .030 SimQINCo .085 .006 .000 .214 .000 .000 .000 .000 .018 .000 .004 .004 .028 RQVAE .059 .006 .000 .200 .000 .000 .000 .000 .026 .001 .004 .004 .025 DiVeQ .052 .000 .000 .103 .000 .000 .000 .000 .031 .003 .014 .015 .018 SF-DiVeQ .023 .002 .000 .156 .000 .000 .000 .000 .016 .005 .014 .011 .019 BSQ .012 .000 .000 .088 .000 .000 .000 .000 .008 .000 .001 .000 .009 LFQ .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 f=8f=8 AEKL .010 .000 .000 .004 .000 .000 .000 .000 .009 .000 .007 .006 .003 SoftVQ .000 .000 .000 .001 .000 .000 .000 .000 .009 .000 .000 .000 .001 VQGAN .000 .000 .000 .004 .000 .000 .000 .000 .014 .001 .016 .016 .004 SimVQ .012 .000 .000 .049 .000 .000 .000 .000 .018 .000 .025 .022 .010 SimQINCo .018 .000 .000 .008 .000 .000 .000 .000 .011 .001 .009 .010 .005 RQVAE .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 DiVeQ .037 .000 .000 .011 .000 .000 .000 .000 .011 .001 .010 .014 .007 SF-DiVeQ .029 .000 .000 .047 .000 .000 .000 .000 .022 .000 .005 .006 .009 BSQ .003 .000 .000 .002 .000 .000 .000 .000 .004 .000 .001 .003 .001 LFQ .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 f=16f=16 AEKL .000 .000 .000 .001 .000 .000 .000 .000 .011 .000 .003 .004 .002 SoftVQ .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 VQGAN .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .001 .001 .000 SimVQ .000 .000 .000 .001 .000 .000 .000 .000 .002 .000 .003 .006 .001 SimQINCo .000 .000 .000 .004 .000 .000 .000 .000 .023 .000 .002 .002 .003 RQVAE .000 .000 .000 .006 .000 .000 .000 .000 .040 .000 .006 .003 .005 DiVeQ .000 .000 .000 .000 .000 .000 .000 .000 .031 .000 .005 .004 .003 SF-DiVeQ .000 .000 .000 .009 .000 .000 .000 .000 .010 .000 .003 .006 .002 BSQ .000 .000 .000 .001 .000 .000 .000 .000 .022 .000 .003 .003 .002 LFQ .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000 Table S25: Per-dataset memorization ratio (↑ ), DINOv2 features. Method Path Chest Derma OCT Pneu Reti Breast Blood Tiss OrgA OrgC OrgS mean f=4f=4 AEKL .843 .882 .846 .854 .875 .865 .771 .884 .826 .822 .812 .814 .841 SoftVQ .832 .873 .852 .846 .883 .854 .786 .873 .790 .814 .809 .813 .835 VQGAN .797 .858 .823 .823 .850 .804 .753 .864 .800 .821 .802 .807 .817 SimVQ .796 .859 .816 .828 .847 .770 .758 .871 .789 .819 .802 .802 .813 SimQINCo .798 .854 .823 .822 .832 .816 .761 .855 .793 .822 .797 .806 .815 RQVAE .791 .854 .804 .820 .848 .800 .745 .851 .793 .815 .793 .797 .809 DiVeQ .806 .858 .821 .835 .847 .794 .764 .850 .792 .820 .804 .808 .817 SF-DiVeQ .808 .857 .825 .828 .844 .785 .767 .858 .796 .822 .797 .811 .816 BSQ .814 .871 .847 .848 .874 .889 .770 .860 .783 .813 .782 .787 .828 LFQ .906 .901 .820 .863 .874 .887 .796 .876 .842 .841 .842 .836 .857 f=8f=8 AEKL .851 .875 .847 .853 .867 .853 .776 .879 .809 .819 .804 .810 .837 SoftVQ .875 .882 .845 .861 .888 .869 .800 .877 .793 .823 .820 .818 .846 VQGAN .872 .869 .838 .851 .851 .844 .768 .874 .794 .807 .797 .790 .830 SimVQ .824 .870 .821 .842 .864 .799 .754 .865 .785 .809 .786 .784 .817 SimQINCo .839 .864 .844 .850 .850 .797 .778 .872 .797 .812 .796 .799 .825 RQVAE .875 .953 .925 .954 .989 .941 .922 .887 .911 .855 .878 .897 .916 DiVeQ .829 .865 .823 .845 .850 .820 .773 .861 .798 .798 .792 .795 .821 SF-DiVeQ .819 .864 .815 .836 .857 .825 .758 .868 .789 .814 .804 .809 .822 BSQ .873 .877 .854 .853 .868 .901 .779 .883 .802 .848 .836 .835 .851 LFQ .902 .932 .850 .885 .889 .920 .828 .895 .851 .873 .866 .836 .877 f=16f=16 AEKL .867 .872 .848 .854 .873 .881 .758 .884 .811 .817 .807 .805 .840 SoftVQ .936 .807 .864 .911 .889 .812 .918 .961 .935 .916 .890 .875 .893 VQGAN .874 .895 .867 .846 .877 .877 .838 .892 .831 .820 .817 .813 .854 SimVQ .874 .882 .856 .861 .880 .889 .827 .884 .829 .814 .802 .812 .851 SimQINCo .878 .873 .853 .856 .870 .871 .813 .883 .797 .806 .807 .806 .843 RQVAE .851 .868 .834 .852 .854 .828 .768 .869 .784 .801 .798 .803 .826 DiVeQ .882 .873 .847 .859 .863 .874 .796 .882 .795 .811 .807 .805 .841 SF-DiVeQ .881 .874 .846 .846 .864 .864 .798 .885 .805 .812 .819 .807 .842 BSQ .881 .883 .852 .866 .871 .860 .787 .885 .793 .827 .826 .815 .845 LFQ .867 .911 .854 .870 .892 .859 .877 .897 .854 .842 .832 .827 .865