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From Inference to Adaptation: A Unified Optimal Transport View of Vision Language Model
Qi Yu, Zhichen Zeng, Katherine Tieu, Xiyuan Yang, Ruizhong Qiu, Yuchen Yan, Lihui Liu, Yanjun Zhao, Lingjie Chen, Jingrui He, Hanghang Tong
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Summary
The paper introduces ORIGIN, a Test-Time Adaptation (TTA) framework for Vision-Language Models (VLMs) that unifies inference and adaptation objectives using Optimal Transport (OT). It addresses the issue of noisy pseudo-labels in existing TTA methods by formulating zero-shot image classification as a cross-modal alignment problem via Wasserstein OT, which provides robust sample-level pseudo-labels. These labels are then used in a soft-label InfoNCE loss for adaptation, explicitly modeling image-text relationships. The authors theoretically prove that the InfoNCE loss is equivalent to an entropic Wasserstein OT formulation, thereby bridging the gap between inference and adaptation objectives. Experiments on CIFAR10-C, CIFAR100-C, and ImageNet-C show ORIGIN outperforms state-of-the-art methods by up to 7% with high efficiency.
Entities (12)
Relation Signals (9)
ORIGIN → evaluatedon → CIFAR100-C
confidence 95% · CIFAR100-C
ORIGIN → evaluatedon → ImageNet-C
confidence 95% · ImageNet-C dataset
ORIGIN → evaluatedon → CIFAR10-C
confidence 95% · extensive experiments on three standard benchmarking datasets... CIFAR10-C
ORIGIN → solves → Test-Time Adaptation
confidence 95% · propose a principled VLM TTA method called ORIGIN
ORIGIN → uses → InfoNCE loss
confidence 95% · adopt a soft-label InfoNCE loss to adapt VLMs
ORIGIN → uses → Optimal Transport
confidence 95% · propose a principled VLM TTA method called ORIGIN... leverages optimal transport (OT)
Qi Yu → affiliatedwith → University of Illinois Urbana-Champaign
confidence 90% · Qi Yu 1... 1 University of Illinois Urbana-Champaign
Optimal Transport → unifies → InfoNCE loss
confidence 90% · theoretically reveal that the InfoNCE loss can be neatly reformulated as a Wasserstein OT formulation
ORIGIN → outperforms → BATCLIP
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Abstract
Abstract:Vision-language models (VLMs) have demonstrated remarkable zero-shot capabilities yet remain sensitive to real-world distribution shifts during inference. Although significant efforts are devoted to adapting VLMs at test time, they rely heavily on noisy pseudo-labels predicted directly from raw embedding similarities during inference, which are unreliable under distribution shift and mislead the adaptation. To avoid noise amplification, existing works craft coarse-grained surrogate objectives during adaptation, which fail to explicitly model sample-level relationships across different modalities, creating objective mismatch with inference, thus leading to marginal performance improvement. In this work, we aim to bridge the detached objectives of inference and adaptation for VLMs, and propose a principled VLM TTA method called \algname. For VLM inference, we formulate the zero-shot image classification task as a cross-modal alignment problem encoded via a Wasserstein OT formulation, providing robust pseudo-labels at the sample-level to effectively adapt VLMs. For VLM adaptation, we adopt a soft-label InfoNCE loss to adapt VLMs based on the OT-induced pseudo-labels, leveraging fine-grained supervisions to explicitly model relationships of individual image-text pairs via contrastive learning, which empowers accurate inference at the same granularity. Moreover, we theoretically reveal that the InfoNCE loss can be neatly reformulated as a Wasserstein OT formulation, thereby unifying the objectives of the inference and adaptation of VLMs to achieve their mutual benefits. Extensive experiments demonstrate the effectiveness and efficiency of our methods, outperforming the best-performing methods by up to 7% with state-of-the-art efficiency.
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- Source: https://arxiv.org/abs/2608.18339v1
- Canonical: https://arxiv.org/abs/2608.18339v1
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From Inference to Adaptation: A Unified Optimal Transport View of Vision Language Model Qi Yu 1∗ Zhichen Zeng 1 Katherine Tieu 1 Xiyuan Yang 1 Ruizhong Qiu 1 Yuchen Yan 2 Lihui Liu 3 Yanjun Zhao 1 Lingjie Chen 1 Jingrui He 1 Hanghang Tong 1 1 University of Illinois Urbana-Champaign 2 Amazon 3 Wayne State University Abstract Vision-language models (VLMs) have demonstrated remarkable zero-shot capabili- ties yet remain sensitive to real-world distribution shifts during inference. Although significant efforts are devoted to adapting VLMs at test time, they rely heavily on noisy pseudo-labels predicted directly from raw embedding similarities during inference, which are unreliable under distribution shift and mislead the adapta- tion. To avoid noise amplification, existing works craft coarse-grained surrogate objectives during adaptation, which fail to explicitly model sample-level relation- ships across different modalities, creating objective mismatch with inference, thus leading to marginal performance improvement. In this work, we aim to bridge the detached objectives of inference and adaptation for VLMs, and propose a principled VLM TTA method called ORIGIN. For VLM inference, we formulate the zero- shot image classification task as a cross-modal alignment problem encoded via a Wasserstein OT formulation, providing robust pseudo-labels at the sample-level to effectively adapt VLMs. For VLM adaptation, we adopt a soft-label InfoNCE loss to adapt VLMs based on the OT-induced pseudo-labels, leveraging fine-grained supervisions to explicitly model relationships of individual image-text pairs via contrastive learning, which empowers accurate inference at the same granularity. Moreover, we theoretically reveal that the InfoNCE loss can be neatly reformulated as a Wasserstein OT formulation, thereby unifying the objectives of the inference and adaptation of VLMs to achieve their mutual benefits. Extensive experiments demonstrate the effectiveness and efficiency of our methods, outperforming the best-performing methods by up to 7% with state-of-the-art efficiency. 1 Introduction Vision-language models (VLMs), such as CLIP [Radford et al., 2021], learn to project image and text embeddings into a shared embedding space, and have achieved remarkable zero-shot capability across diverse multimodal learning tasks, such as image classification [Radford et al., 2021], image captioning [Li et al., 2022], and semantic segmentation [Lüddecke and Ecker, 2022]. Despite the success of pre-trained VLMs, the aligned embedding spaces are vulnerable to real-world distribution shifts, such as image corruption [Hendrycks and Dietterich, 2019], causing significant performance degradation of VLMs at deployment. To mitigate this issue, a predominant approach is to adapt pre-trained VLMs at test time, i.e., test-time adaptation (TTA), based on unlabeled test data. This paradigm allows pre-trained VLMs to adapt dynamically to shifted domains at deployment without accessing large-scale source training data or test labels. Although existing TTA methods have demonstrated strong improvement across different benchmarks, they bear the following two key limitations which lead to suboptimal adaptation performance. Firstly ∗ Correspondence to: Qi Yu <qiyu6@illinois.edu> Preprint. arXiv:2608.18339v1 [cs.CV] 18 Aug 2026 0510152025 # Batches 60 65 70 75 80 Accuracy (%) CIFAR10-C 0510152025 # Batches 36 38 40 42 44 46 48 CIFAR100-C OT + InfoNCE (ORIGIN)Emb + InfoNCEOT + BATCLIPEmb + BATCLIP Figure 1: Training dynamics of different combinations of inference and adaptation objective on CIFAR10-C. (1) Embedding-based inference are consistently outperformed by OT-based inference under the same loss function, and may even leads to performance degradation during adaptation due to excessive noise amplification; (2) ORIGIN adopts InfoNCE loss with OT-induced pseudo-labels to explicitly model sample-level relationships across modalities, increasing accuracy monotonically during adaptation and consistently achieves the best performance. (Limitation #1), existing TTA methods predominantly rely zero-shot predictions of VLMs inferred from the raw embedding similarity of images and texts under distribution shifts, thus generating noisy and unreliable pseudo-labels that later limit or even misguide the adaptation of pre-trained VLMs [Shu et al., 2022a, Li et al., 2024a, Sheng et al., 2025]. As shown in Table 2 and Figure 1, pseudo-labels inferred from raw embedding similarities suffer from poor accuracy, leading to suboptimal or even degraded performance during adaptation. Secondly (Limitation #2), limited by the noisiness of pseudo-labels, existing TTA methods rely heavily on crafting surrogate objectives on aggregated class-level prototypes (e.g., average embedding of a class) [Maharana et al., 2025, Bao et al., 2025] to avoid excessive noise amplification. However, class- level supervisions are inherently coarse-grained, treating individual samples uniformly. Therefore, they fail to model cross-modal relationships between individual image-text pairs, which inherently limits the adaptation performance evaluated on sample-level alignment tasks during inference. As shown in Figure 1 and Table 2, while the objective of BATCLIP [Maharana et al., 2025], the best- performing baseline, can sometimes avoid noise amplification during adaptation, its performance are inherently limited by the class-level design of its adaptation objective. In this paper, we propose a principled VLM TTA framework which leveragesoptimal transport (OT) to bridge theinference and adaptationof VLMs at test time, called ORIGIN. At the inference stage, we formulate the zero-shot image classification task as an alignment problem across the image and text modalities, whose results are inferred from the transport plan of a Wasserstein OT formulation. Empowered by the global view and constrained nature of OT [Chen et al., 2020, Yu et al., 2025b, Zhu et al., 2025, Yu et al., 2025a], predictions inferred from the solved transport map is significantly more accurate than that inferred from raw embedding similarities, as shown in Table 2, therefore generating more robust and reliable pseudo-labels for TTA (Limitation 1). At the adaptation stage, equipped with the reliable pseudo-labels derived from the Wasserstein OT formulation, we directly adopt the soft-label InfoNCE loss, aligning with the pre-training objective of VLMs, to explicitly model the embedding relationships of image-text pairs via contrastive learning, leverging fine-grained supervision signals to unleash the full potential of test data for adapting the model at test time (Limitation 2). As shown in Figure 1, ORIGIN adopts the soft-label InfoNCE loss with OT-induced pseudo-labels, guiding the adaptation effectively and leading to consistent improvement in accuracy. Finally, to further bridge the test-time inference and adaptation of VLMs, we theoretically prove that the InfoNCE loss can be reformulated to an entropic Wasserstein OT formulation. In this way, the inference and adaptation of VLMs are no longer decoupled stages but a mutually beneficial process with a shared objective function through the lens of OT. While robust and reliable pseudo-labels produced at the inference stage help improve the adaptation of VLMs, effective adaptation of VLMs also aligns disparate embeddings of text and image modalities under distribution shifts, thus improving 2 the inference performance. By alternating between optimizations of the OT transport plan and the parameters of VLMs, we achieve the mutual benefits of robust inference and fine-grained adaptation, which maximally improve the TTA performance of VLMs. To evaluate the effectiveness of our proposed ORIGIN, we conduct extensive experiments on three standard benchmarking datasets, showing that our method significantly outperforms state-of-the-art TTA methods with up to 7% mean accuracy improvement without additional latency. Our main contribution are summarized as follows: •Unified View. To our best knowledge, we are the first to theoretically bridge the inference and adapation of VLMs at test-time through the lens of optimal transport. •Novel Methodology. We proposed a novel VLM TTA methods based on optimal transport which aligns the loss functions of adaptation with the pretraining objective of VLMs. •Strong Performance. Extensive experiments on three standard VLM TTA benchmarks demonstrate significant performance gain compared to state-of-the-art baselines. 2 Preliminaries In this section, we first introduce preliminaries on VLM TTA in Section 2.1, followed by optimal transport in Section 2.2. In this paper, we use bold uppercase letters for matrices (e.g.,S), bold lowercase letters for vectors (e.g.,μ), calligraphic uppercase letters for sets (e.g.,T) and lowercase letters for scalars (e.g., k). 2.1 Test-time Adaptation of VLMs We denote the text space byTand image space byV. A pre-trained VLM consists of a text encoder f φ : T →R d and an image encoderf θ : V →R d , which map images and texts into a shared embedding space of dimensiond. For a zero-shot image classification task withndifferent classes, the image encoderf θ projects an imagevto an embeddingv∈R d , and the text encoderf φ projects text descriptions ofcdifferent classes, e.g., "a photo of a <class>" to embeddingst j ∈R d c j=1 . Predictions are inferred by comparing the embedding similarity of the test image and text descriptions of different classes, e.g.,arg max j v ⊤ t j . In this paper, we consider the online TTA setting, where test images under distribution shifts arrives sequentially in a batch manner [Maharana et al., 2025]. 2.2 Optimal Transport OT is becoming a popular and effective tool for aligning distributional structures [Santambrogio, 2015]. Formally, letμ = P n i=1 μ i δ x i andν = P m j=1 ν i δ y j be two discrete probability distributions whereδdenotes the Dirac measure, the discrete OT problem seeks an optimal transport planSthat minimizes the total transport cost as follows: min S∈Π(μ,ν) ⟨C,S⟩(1) whereΠ(μ,ν) := S∈R n×m + |S1 m =μ,S ⊤ 1 n =ν , andC∈R n×m is the cost matrix measur- ing the cost of transporting mass from different units of supports. The optimal value of Eq.(1)defines the Wasserstein distance betweenμandνunder the cost matrixC, and the resulting transport plan encodes the soft correspondence between points from the two distributions. To solve the Wasserstein OT formulation efficiently, [Peyré and Cuturi, 2019] introduces entropic regularization into Eq. (1) to approximate the original OT formulation: min S∈Π(μ,ν) ⟨C,S⟩− εH(S)(2) whereH(S) := − P i,j S i,j (log S i,j − 1)andε > 0denotes the entropic regularization weight. Eq.(2)yields anε-strongly convex optimization problem solvable via the Sinkhorn algorithm with a quadratic complexity [Nemirovski and Rothblum, 1999]. Specifically, The optimal solution of Eq.(2) yields the following scaling form: S ∗ = diag(a)K diag(b),(3) whereK := exp(−C/ε)is the Gibbs kernel, andμ ∈R n + ,ν ∈R m + are scaling vectors which enforce the marginal constraints. The Sinkhorn algorithm solves forμandνvia iterative matrix scaling: a (t+1) =μ⊘ (Kb (t) ), b (t+1) =ν⊘ (K ⊤ a (t+1) ),(4) where⊘ denotes element-wise division. 3 Test Images a photo of a + cat truck ... Text Descriptions Text Encoder Image Encoder 퐂 !" =1−풗 ! # 풕 " 휇 $ 휇 ! Sinkhorn 퐒 풗 ! ! % 풕 " " & Embeddings VLM Inference Unified Objective Entropic Wasserstein OT / InfoNCE KL( || ) 퐒 퐏 ' Soft pesduo-labels 퐏 !," ' = exp(풗 ! # 풕 " ) 푏 ∑ exp(풗 ! # 풕 ) ) & ) forzen tuned otherlayers normlayers VLM Adapation Figure 2: An overview of ORIGIN. VLMs first encode test images via the image encoder and text descriptions of different classes via the text encoder. During inference, ORIGIN infers zero-shot image classification by solving an entropic Wasserstein OT problem. During adaptation, ORIGIN explicitly models the embedding relationships of shifted modalities at the sample-level via a soft-label InfoNCE loss, and optimizes normalization layers of the image encoder. 3 Methodology In this section, we present the proposed ORIGIN. We first introduce a Wasserstein OT formulation which predicts image-text alignment robustly during inference, in Section 3.1. Then, we introduce the adopted soft-label InfoNCE during adaptation which explicitly models sample-level relationships via contrastive learning, in Section 3.2. Finally, we theoretically unifies the objectives of ORIGIN at the inference and adaptation stage, in Section 3.3. An overview of ORIGIN is shown in Figure 2. 3.1 OT-based Inference Pre-trained VLMs are trained to project different modalities, i.e., images and texts, into the same embeddings space, making them directly comparable based on embedding similarities. However, the unified embedding space of VLMs are vulnerable under distribution shifts, making embedding similarities noisy to infer the actual semantic similarity between shifted images and texts. OT, in contrast, leverages a constrained optimization framework to produce noise-reduced similarity across different modalities [Chen et al., 2020]. Therefore, at the inference stage of VLMs, we propose to use the raw embedding distances across shifted modalities as their transport cost at a distribution level, and instead infer image-text alignment by solving an entropic Wasserstein OT formulation in Eq.(5). Formally, given a batch of test imagesV := v i b i=1 of sizeband a set of text descriptionsT := t j c j=1 ofcdifferent text classes, we predict image-text alignment by solving the following entropic Wasserstein OT formulation: min S∈Π(μ i ,μ t ) ⟨C,S⟩− εH(S) C i,j := 1− v ⊤ i t j (5) wherev i = f θ (v i ),t j = f φ (t j ). As we will show later in Section 3.3, such cost design provides a unified view of VLM inference and adaption.μ i andμ t are two marginal distributions defined over the image batch and text classes respectively. We assume a uniform distribution at the image level, i.e.,μ i := P b i 1 b δ v i , treating each test image with equal importance. For text-level distribution μ t , we assume a uniform distribution before adaptation and dynamically adjustμ t according to the predictions of previous test batches by exponential moving average (EMA), i.e., μ (k) t = α ˆ μ (k−1) t + (1− α)μ (k−1) t μ (0) t := c X i=1 1 c δ t i (6) whereμ (k) t denotes the text-level marginal distribution for OT, and ˆ μ (k−1) t denotes the predicted text label distribution at the (k-1)-th batch.αis the EMA parameter. For a test imagev i , its predicted label ̃c i based on image-text alignment is inferred from the solved transport mapS ∗ , i.e., ̃c = arg max j S ∗ i,j . 4 Eq.(5)yields anε-strongly convex optimization problem that can be solved more efficiently via the Sinkhorn algorithm [Peyré and Cuturi, 2019], as shown in Eq. (3) and Eq. (4). Instead of relying on noisy embedding similarities which are unreliable under distribution shifts, ORIGIN infer image-text alignment from a global view by leveraging the constrained nature of OT [Chen et al., 2020, Zhu et al., 2025, Yu et al., 2025b], therefore leading to more accurate predictions which produces robust and reliable pseudo-labels for VLM adaptation. 3.2 Fine-grained Adaptation Empowered by the robust predictions of test image labels via OT, ORIGIN directly adopts a soft-label InfoNCE loss for image-to-text alignment as the optimization objective during adaptation, modeling cross-modal relationships explicitly at the same sample-level as VLM inference. Formally, for a batch of test imageV :=v i b i and a set of text descriptionsT :=t j c j ofcdifferent text classes, ORIGIN optimizes the following soft-label InfoNCE loss in Eq. (7). min θ KL(S∥ ̃ P θ ), ̃ P θ i,j := exp(v ⊤ i t j /τ ) b P c k=1 exp(v ⊤ i t k /τ ) (7) whereKL(·∥·)denotes the KL divergence,Sis the transport map of OT at the inference stage serving as soft pseudo-labels, and τ is a scalar temperature. Recall that the pre-training objective of CLIP consists of two hard-label InfoNCE losses which simultaneously conduct image-to-text and text-to-image alignment in the embedding space, as shown in Eq. (8) [Shi et al., 2024] min θ KL(P∥ ̃ P θ,φ ) + KL(P∥ ˆ P θ,φ )(8) wherePconsists of one-hot vectors denoting hard alignment of paired images and texts, and ̃ P θ,φ , ˆ P θ,φ are defined as follows ̃ P θ,φ i,j := exp(v ⊤ i t j /τ ) b P c k=1 exp(v ⊤ i t k /τ ) , ˆ P θ,φ i,j := exp(v ⊤ i t j /τ ) c P b k=1 exp(v ⊤ k t j /τ ) (9) Comparing Eq.(7)and Eqs.(8)-(9)reveals that the adaptation objective of ORIGIN essentially 1) replaces ground-truth hard label ofPwith OT-induced soft pseduo-labelSsince test labels are unavailable during inference at test-time, and 2) solely adapts image encoder and aligns shifted image embeddings to text embeddings since distribution shifts typically happens on the image side [Bao et al., 2025, Maharana et al., 2025]. In this way, ORIGIN aligns with the core philosophy of the pre-training of CLIP, which explicitly models embedding relationships of individual image-text pairs via contrastive learning, thus guiding the adaptation of VLMs effectively to enhance the its inference capability under distribution shifts. While we only adapt the InfoNCE loss at image-to-text alignment level, our framework can be naturally extends to the full InfoNCE loss adopted for the pre-training of CLIP by adding the text-to-image alignment counterpart, e.g., under text-level distribution shifts. 3.3 Bridging Inference and Adaptation via OT In this section, we further bridge the inference and adaptation objectives of VLMs theoretically through the lens of OT. Specifically, as shown in the following lemma, the soft-label InfoNCE loss in Eq. (7) is mathematically equivalent to the entropic Wasserstein OT formulation in Eq. (5). Lemma 3.1. Given C i,j = 1− v ⊤ i t j , the term KL(S∥ ̃ P θ ) in Eq. (7) can be formulated as follows KL(S∥ ̃ P θ ) = 1 τ (⟨C,S⟩− τH(S)) |z entropic Wasserstein OT + 1 + 1 b b X i=1 log " b c X k=1 exp v ⊤ i t k − 1 τ # |z constant w.r.t.S (10) Detailed proof of Lemma 3.1 can be found in Appendix A.1. We can see from Eq.(10)thatKL(S∥ ̃ P θ ) can be rewritten into a entropic Wasserstein OT term plus a constant w.r.t. the transport planSwhich does not affect the optimization ofS. Therefore, optimizing Eq.(10)w.r.t. the transport planSis equivalent to optimizing Eq. (5), i.e., min S∈Π(μ i ,μ t ) KL(S∥ ̃ P θ ) :=min S∈Π(μ i ,μ t ) ⟨C,S⟩− τH(S)(11) 5 with the scalar temperatureτin Eq.(7)becoming the entropic regularization weightεin Eq.(5), i.e.,ε := τ. In this way, we theoretically prove that the inference and adaptation of VLMs by the proposed ORIGIN share the same objective functions w.r.t. different optimized variablesSand the parameterθof the image encoder, implying that these two processes are mutually beneficial instead of decoupled from each other. For one thing (inference for adaptation), OT estimate robust soft pseudo-labels at the sample-level which guides the adaptation of VLMs effectively; for another (adaptation for inference), the InfoNCE loss aligns with the pre-training philosophy of CLIP, which explicitly models sample-level relationships across modalities and effectively guides the re-alignment of image and text embeddings under distribution shift, generating accurate predictions for improved inference. By alternate between optimizations ofSandθ, ORIGIN achieves mutual benefits of OT-based inference and InfoNCE-based adaptation, leading to effective TTA of VLMs. Formally, the unified objective of inference and adaptation in ORIGIN at test time is introduced as follows. min θ,S∈Π(μ i ,μ t ) KL(S∥ ̃ P θ ) ̃ P θ i,j := exp(v ⊤ i t j /τ ) b P c k=1 exp(v ⊤ i t k /τ ) (12) Note that the soft-label InfoNCE loss on the text side can also be unified with a entropic Wasserstein OT formulation in a similar fashion, making our unified theory of inference and adaptation of VLMs applicable to both adaptation settings under image and text-level distribution shifts. 4 Experiments In this section, we carry out comprehensive experiments and analyses to evaluate the proposed ORIGIN from the following aspects: • Q1: How effective is ORIGIN compared to state-of-the-art methods under distribution shifts? • Q2: How does ORIGIN trade off effectiveness and efficiency? • Q3: How does inference and adaptation of ORIGIN benefit each other under a unified OT view? • Q4: How sensitive is ORIGIN to different hyperparameter and design choices? Due to limited space, we include detailed experimental setup in Appendix B, including introductions of datasets & metrics, VLM backbones, TTA baselines, reproducibility details, and machines used for conducting all experiments. 4.1 Benchmarking Results We first benchmark ORIGIN with ViT-B-16 visual encoder on three standard VLM TTA benchmarks, whose results are reported in Table 1. We observe that (1) The proposed ORIGIN consistently achieve state-of-the-art performance across all three benchmarks. Specifically, on datasets with low-resolution images, ORIGIN outperforms the best competitor by a large margin, with a 7.4% and 4.8% improvement in mean accuracy on CIFAR10-C and CIFAR100-C, respectively. For the larger-scale ImageNet-C dataset, ORIGIN also achieve the best mean accuracy with at least 2.4% performance improvement, demonstrating the effectiveness of ORIGIN. (2) OT inherently produces accurate predictions without adapting VLM parameters. Comparing the performance of OT inference without adaptation in Table 2, with that of training-free baselines (TDA, DMN, VTE, ZERO, ECALP, and TENT), shows that OT inference alone outperforms all training-free heuristics in mean accuracy on CIFAR10-C, revealing that OT itself can infer accurate predictions, thus generating robust pseudo-labels that leads to effective adaptation. (3) The InfoNCE loss re-aligns image and text embeddings of the same class effectively under distribution shifts. As shown in Figure 3, the proposed ORIGIN produces image embeddings that not only align closely with the text embeddings of the same class, but also show clear clustering structures in the embedding space. In contrast, coarse-grained surrogate loss functions of other baselines leads to entangled image embeddings which deviated from their corresponding text embeddings, harming the adaptation performance. 4.2 Efficiency Results We study the effectiveness-efficiency trade-off of the proposed ORIGIN and other training-based TTA methods, including RoTTA, TPT, MEMO, WATT, MINT and BATCLIP, on CIFAR10-C and CIFAR100-C. The results on mean accuracy vs. average runtime per corruption, defined as the averaged total amount of time required for inference and adaptation over different corruption types, are shown in Figure 4. We can see that ORIGIN achieve state-of-the-art effectiveness and 6 Table 1: Benchmarking results with ViT-B-16. The 1st/2ndbest results are highlighted in bold and underline, respectively. Additional benchmarking results with ViT-B-32 are shown in Table 4 Dataset Method NoiseBlurWeatherDigital Mean Gauss. Shot Impul. Defoc. Glass Motion Zoom Snow Frost Fog Brit. Contr. Elast. Pixel. JPEG CIFAR10-C Source37.7 42.0 54.271.840.968.174.0 74.1 77.1 70.6 84.0 62.753.6 47.2 59.0 61.2 TDA40.9 44.0 50.572.344.671.775.6 75.5 78.2 71.6 85.7 62.456.3 48.3 58.1 61.9 DMN43.0 47.4 53.873.540.071.976.3 74.5 76.2 71.0 84.2 60.254.4 47.2 57.0 62.4 VTE42.8 46.7 63.971.045.669.073.6 76.7 78.5 71.0 85.7 57.559.5 60.8 61.7 64.3 ZERO38.7 43.9 57.371.740.969.074.5 74.5 77.6 72.7 84.1 60.355.5 48.6 61.8 61.6 ECALP46.5 50.8 61.171.342.070.874.9 75.9 79.0 71.1 86.3 60.857.9 49.5 61.4 64.2 TENT15.2 18.0 38.281.7 21.376.382.284.081.8 80.490.280.263.4 58.5 56.5 61.4 RoTTA39.2 43.1 55.471.841.368.374.0 74.3 77.8 70.9 85.0 63.454.2 49.1 60.3 62.3 TPT38.1 42.4 60.773.344.969.575.8 76.1 78.5 71.9 85.6 62.458.9 55.2 62.5 64.0 MEMO38.1 41.5 55.472.141.168.973.9 75.1 77.7 71.7 84.5 62.056.0 49.0 61.3 62.3 WATT46.3 53.3 59.975.238.371.976.2 77.3 80.7 76.1 87.9 75.755.1 62.4 63.2 66.7 MINT54.3 58.5 65.077.049.077.979.0 82.0 81.3 77.2 89.5 74.361.7 61.4 64.3 70.0 BATCLIP 62.365.066.679.855.980.481.6 82.0 83.980.4 88.5 81.569.363.167.773.5 ORIGIN71.8 74.3 77.784.170.584.185.4 86.6 86.5 87.1 90.9 89.376.9 81.1 74.7 80.9 CIFAR100-C Source19.8 21.3 24.942.720.343.548.3 48.4 49.7 41.4 56.7 34.529.1 23.8 32.4 35.3 TDA22.4 25.5 29.343.119.443.549.1 48.1 50.7 41.5 58.4 35.229.0 24.4 32.9 36.5 DMN21.9 25.4 25.141.116.343.449.1 45.6 48.4 39.8 57.9 32.425.9 23.4 30.8 35.1 VTE18.0 18.9 27.939.919.539.545.3 48.6 46.6 40.5 55.0 30.132.2 30.4 31.3 34.6 ZERO19.0 20.6 28.643.719.443.149.1 48.8 50.0 44.4 57.7 35.031.2 25.0 33.6 36.8 ECALP23.4 25.3 30.543.019.542.849.6 47.8 50.3 42.7 58.0 35.130.0 25.4 31.9 37.0 TENT7.47.78.851.88.352.253.8 52.5 36.7 48.0 63.152.936.539.538.236.7 RoTTA20.9 22.6 26.542.820.443.348.2 49.1 49.8 41.5 57.7 34.528.8 25.5 33.3 35.8 TPT18.3 19.5 27.643.619.642.348.2 48.8 49.1 42.0 57.6 33.131.2 27.3 32.9 36.3 MEMO19.8 22.4 27.643.620.044.449.1 50.5 50.0 43.4 58.9 34.630.4 25.4 33.7 36.7 WATT25.8 27.3 31.848.423.448.952.7 53.3 52.2 48.1 62.9 45.635.4 37.0 38.1 42.0 MINT27.930.435.848.926.147.353.3 52.6 52.548.464.4 43.935.2 32.6 35.2 42.2 BATCLIP 25.5 28.4 34.250.026.648.755.2 51.9 51.5 48.3 62.3 45.934.4 33.0 36.8 42.5 ORIGIN36.9 39.1 44.750.636.251.454.453.9 53.0 52.0 61.7 53.241.4 45.8 42.3 47.3 ImageNet-C Source11.4 12.9 11.923.315.424.922.2 32.0 29.9 35.6 54.4 17.312.7 30.9 33.5 24.3 TDA12.3 14.4 14.824.216.826.423.7 33.1 32.538.5 55.2 19.314.5 33.9 34.8 26.7 DMN11.5 13.9 14.422.316.224.422.7 31.7 30.8 35.8 53.9 16.012.9 32.7 25.3 24.0 VTE9.210.8 11.024.414.624.825.3 35.1 32.1 37.9 55.1 15.914.7 38.8 33.9 25.4 ZERO10.3 11.4 11.324.714.624.322.8 32.7 30.4 36.7 54.5 17.213.4 34.4 32.5 24.4 ECALP13.3 15.2 13.622.115.125.623.4 30.8 30.2 35.6 51.9 18.513.1 33.6 33.6 25.4 TENT5.55.37.925.519.526.824.3 33.8 30.8 38.3 54.6 22.613.9 34.8 35.6 25.2 RoTTA10.9 12.7 12.523.615.824.922.4 32.1 29.6 36.2 53.9 17.212.6 31.1 33.1 25.1 TPT8.19.410.423.615.224.924.4 34.4 32.3 36.9 55.1 16.114.2 34.1 33.8 24.7 MEMO10.6 12.0 11.923.715.524.723.2 32.9 29.8 35.9 54.3 17.312.3 31.6 33.0 25.1 WATT11.4 13.1 13.325.618.426.825.0 33.4 29.8 37.9 53.9 21.415.4 33.2 34.8 25.9 MINT19.7 19.9 19.226.5 21.629.625.6 32.3 29.3 39.3 55.324.018.8 36.2 38.2 29.3 BATCLIP 19.720.919.426.121.130.428.835.431.2 40.555.6 26.024.136.9 37.4 30.5 ORIGIN23.0 24.3 23.727.626.631.331.4 38.0 34.1 40.6 50.2 32.331.5 38.438.032.9 RoTTAMINTBATCLIPORIGIN Figure 3: Embedding visualization of different VLM TTA methods by t-SNE on CIFAR10-C. Stars denote text embeddings of different classes, and round points denote image embeddings. efficiency simultaneously, with the corresponding data points lying consistently on the upper-left region of both scatter plots. Specifically, ORIGIN outperforms the fastest baselines with up to 7.4% improvement in mean accuracy without additional latency. Compared with the remaining training-based methods, ORIGIN consistently outperforms all of them with up to 45×speed-up in runtime. This demonstrates that the additional overheads of solving the entropic Wasserstein OT during inference are practically negligible compared to the adaption of VLM parameters, which requires expensive forward and backward propagation, making ORIGIN surprisingly efficient. 7 10 1 10 2 10 3 Average Runtime Per Corruption (s) 62.5 65.0 67.5 70.0 72.5 75.0 77.5 80.0 Mean Accuracy (%) 44× 7.4% CIFAR10-C 10 1 10 2 10 3 Average Runtime Per Corruption (s) 36 38 40 42 44 46 45× 4.8% CIFAR100-C RoTTATPTMEMOWATTMINTBATCLIPORIGIN Figure 4: Accuracy vs. runtime trade-off of ORI- GINand other training-based TTA methods, show- ing that the proposed ORIGIN achieves SOTA effectiveness and efficiency at the same time. Table 2: Accuracy (%) of different variants of ORIGIN on CIFAR10-C. DatasetCIFAR10-C Corruption NoiseBlurWeather Digital Mean EMB44.6963.5476.4755.8360.13 OT54.1865.8379.1062.4065.38 EMB+M59.2770.7382.5065.4369.48 EMB+B62.9473.4083.6168.9972.24 EMB+I37.9971.2883.5667.3365.04 OT+M62.3171.8982.9567.8271.24 OT+B65.5174.7783.4671.9373.92 ORIGIN74.4381.0587.6080.4480.88 4.3 Further Studies 4.3.1 Mutual Benefit of Inference and Adaptation To isolate the individual effect of OT and InfoNCE loss at the inference and adaptation stage, and verify that they are mutually beneficial for VLM TTA, we compare the performance of ORIGIN against the following variants on CIFAR10-C: • EMB / OT: Embedding-based / OT-based inference without adaptation. • EMB+M: embedding-based inference with the adaption loss of MINT [Bao et al., 2025]. •EMB+B: embedding-based inference with the adaption loss of BATCLIP [Maharana et al., 2025]. • EMB+I: embedding-based inference with the InfoNCE loss. • OT+I: OT-based inference with the adaption loss of MINT [Bao et al., 2025]. • OT+B: OT-based inference with the adaption loss of BATCLIP [Maharana et al., 2025]. • ORIGIN: OT-based inference with the InfoNCE loss. The results are shown in Tables 2. (1) OT-based inference predict reliable pseudo-labels which leads to consistent performance improvement. Specifically, comparing the first three rows of Tables 2 with the last three rows reveals that OT-based inference consistently outperforms embedding- based inference under the same adaption loss, with an average performance improvement of 1.78%, 1.68%, and 15.84%. This demonstrates that OT consistently infer robust pseudo-labels during adapta- tion which leads to effective adaptation at test-time. (2) InfoNCE loss improves the performance upperbound of TTA. While class-level surrogate loss functions of MINT and BATCLIP sometimes avoid noise amplification inside pseudo-labels, the InfoNCE loss contributes to a higher performance upper-bound with an average performance improvement of 9.64% over MINT and 6.96% over BATCLIP when supervised by OT-induced pseudo-labels, demonstrating the necessity of explicit modeling of sample-level relationships across different modalities. (3) OT-based inference and the InfoNCE-based adaptation are mutually beneficial under a unified formulation. The proposed ORIGIN, which theortically bridges the inference and adaptation objectives, consistently achieves the best performance, demonstrating that OT-based inference and InfoNCE-based adaption inherently benefit each other. 4.3.2 Hyperparameter Analysis We study the sensitivity of ORIGIN to three different hyperparameters on CIFAR10-C: the tempera- tureτin Eq.(7)(i.e., the entropic regularization weightεin Eq.(5)), the EMA parameterαin Eq.(6), and the batch sizeb. In general, the performance of ORIGIN remains stable under different choices of hyperparameters with consistent outperformance than its best competitors. Detailed analysis for each parameter are provided as follows. Temperatureτ. We find that overly small or largeτtypically leads to a slight performance degradation for ORIGIN. A smallτsharpens the softmax distribution and enforces deterministic OT prediction, but could potentially introduces errors due to overconfidence. A largeτavoids overly confident prediction, but leads to noisy supervision signals which limits the adaptation performance. Temperatureα.We can see that ORIGIN remain insensitive to different choices ofαthat trade-off historical and current text-level distribution, with less than 1% performance variation. 8 0.10.010.0010.0001 temperature ( / ) 68 70 72 74 76 78 80 82 Mean Accuracy (%) 0.10.30.50.70.9 EMA parameter ( ) 50100200400 batch size (b) MINTBATCLIP Figure 5: Hyperparameter sensitivity study of ORIGIN on CIFAR10-C Batch sizeb.The influence of batch sizebshares similar features as that ofτ, where overly small or largebleads to performance degradation. Smallballows fine-grained adaption but provides limited global information for OT-based inference per batch. By contrast, largebleads to more accurate OT-based inference on a batch level but allows limited steps for adaption. 5 Related Works VLM Test-time Adaptation. VLM TTA adapts pre-trained VLMs like CLIP [Maharana et al., 2025] from the source domain to target domain featured by distribution shifts at test time, without access to source training data or test labels. Early TTA methods for VLMs focus primarily on prompt optimization [Shu et al., 2022a, Xiao et al., 2025], memory management for historical samples [Karmanov et al., 2024, Zhang et al., 2024, Li et al., 2024b], or data augmentation & selection [Döbler et al., 2024], without adapting parameters inside different encoders of VLMs. While efficient, their performance are inherently limited without parameter adaptation. More recent efforts attempt to adopts normalization layers of the encoders inside VLMs by crafting coarse-grained surrogate loss functions. Specifically, BATCLIP [Maharana et al., 2025] adapts both the image and text encoders of CLIP by simultaneously separating image prototypes and aligning image-text prototypes. MINT [Bao et al., 2025] encourage inter-class separability based on averaged image embeddings. However, they overly relies on noisy-pseudo labels to provide coarse-grained supervision and fails to explicitly model cross-modal relationship at sample-level, leading to suboptimal adaptation performance. Optimal Transport for VLMs. OT has attracted increasing attention in multimodal learning and vision-language models. PLOT [Chen et al., 2022] and Prompt-OT [Chen et al., 2026] leverages OT for prompt learning to improve VLMs on downstream vision-language tasks. SWAB [Yi et al., 2024] selects suitable VLMs for zero-shot classification by bridging the statistical gap across the open-source and target datasets via OT. OT-CLIP [Shi et al., 2024] leverages different variants of OT to improve the pretraining performance of CLIP, while OTCCLIP [Zhang et al., 2025] improves the robustness of CLIP against data poisoning with OT-based alignment at pretraining. While OT has been widely adopted for VLMs, none of existing work bridges the inference and adaptation of VLMs at test time through the lens of OT from a theoretical perspective. 6 Conclusion In this paper, we study the VLM TTA problem by theoretically bridging the inference and adaptation of VLMs at test time through the lens of optimal transport to achieve their mutual benefits. To improve the robustness of pseudo-labels during inference, we reformulate the inference of VLMs into a Wasserstein OT formulation, generating reliable pseudo-labels at sample-level for effective adaptation. To leverage fine-grained supervision signals during adaptation, we adopt a soft-label InfoNCE loss to explicitly model cross-modal relationships at the sample-level via contrastive learning, effectively improving adaptation performance which further empowers robust inference at the same granularity. Finally, we theoretically unified the inference and adaptation objectives of VLMs, demonstrating that they inherently benefit each other rather than being decoupled stages. Extensive experiments demonstrate that ORIGIN significantly outperforms the best competitor in mean accuracy with state-of-the-art efficiency. 9 Acknowledgments and Disclosure of Funding Use unnumbered first level headings for the acknowledgments. All acknowledgments go at the end of the paper before the list of references. Moreover, you are required to declare funding (financial activities supporting the submitted work) and competing interests (related financial activities outside the submitted work). More information about this disclosure can be found at:https: //neurips.c/Conferences/2026/PaperInformation/FundingDisclosure. Do not include this section in the anonymized submission, only in the final paper. 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Given that the transport planSis a probability matrix with a uniform marginal distribution at the image side, i.e., P i,j S i,j = 1, P c j=1 S i,j = 1 b , andH(S) :=− P i,j S i,j (log S i,j − 1), the term KL(S∥ ̃ P θ ) in Eq. (7) can be expanded as follows KL(S∥ ̃ P θ ) = b X i=1 c X j=1 S i,j log S i,j ̃ P θ i,j = b X i=1 c X j=1 S i,j log S i,j − b X i=1 c X j=1 S ij " v ⊤ i t j τ − logb− log c X k=1 exp v ⊤ i t k τ # = b X i=1 c X j=1 S i,j log S i,j − 1 τ b X i=1 c X j=1 S i,j (1− C i,j ) + logb + b X i=1 c X j=1 S i,j log c X k=1 exp v ⊤ i t k τ = 1 τ ⟨C,S⟩− H(S) + 1− 1 τ + logb + b X i=1 1 b log c X k=1 exp v ⊤ i t k τ = 1 τ (⟨C,S⟩− τH(S)) + 1 + 1 b b X i=1 log " b c X k=1 exp v ⊤ i t k − 1 τ # In this way, we have proven Lemma 3.1. B Detailed Experimental Setup Datasets & Metrics. We adopt three standard benchmarks for corrupted image classification: CIFAR10-C [Krizhevsky et al., 2009], CIFAR100-C [Hendrycks and Dietterich, 2019], and ImageNet- C [Deng et al., 2009], which share the same 15 different types of corruptions. Following the standard TTA protocol [Wang et al., 2020], all results reported are based on the highest severity level (Level 5). We adopt the classification accuracy as the evaluation metric [Maharana et al., 2025]. VLM Backbones.We adopt the CLIP [Radford et al., 2021] model with different visual encoders, including ViT-B-16 and ViT-B-32. ViT-B-16 is adopted as default unless noted otherwise. Table 3: Detailed hyperparam- eter settings of ORIGIN. Hyperparameters α τ /ε CIFAR10-C0.5 0.01 CIFAR100-C0.5 0.01 ImageNet-C0.3 0.01 VLM TTA Baselines.We compare ORIGIN against state-of-the- art VLM TTA approaches. For training-free methods which relies on memory management or data augmentation, we include TDA [Kar- manov et al., 2024], DMN [Zhang et al., 2024], VTE [Döbler et al., 2024], ZERO [Farina et al., 2024], ECALP [Li et al., 2024b], and TENT [Wang et al., 2020]. For training-based methods that op- timizes prompts or tunable parameters inside VLMs during adap- tation, we include RoTTA [Yuan et al., 2023], TPT [Shu et al., 2022b], MEMO [Zhang et al., 2022], WATT [Osowiechi et al., 2024], MINT [Bao et al., 2025], and BATCLIP [Maharana et al., 2025]. 13 Reproducibility.For all experiments, the reported results are averaged against 5 different runs with randomized data loader. To ensure a fair comparison, all baselines are evaluated on a dataset under the same batch sizeb, which is 200 for CIFAR10-C and CIFAR100-C, and 64 for ImageNet-C. Hy- perparameters of all baselines VLM TTA methods are set as default in their official implementations. Detailed hyperparameter values of ORIGIN are listed in the following Table 3. For all training-based TTA methods, the AdamW optimizer is used with a learning rate of 5e-3 to adapt the VLMs. Machine. All experiments are conducted on a server with dual Intel® Xeon® Gold 6240R CPUs and 4 NVIDIA Tesla V100-SXM2 32GB GPUs. C Additional Experimental Results Table 4: Benchmarking results with ViT-B-32. The 1st/2ndbest results are highlighted in bold and underline, respectively. The proposed ORIGIN consistently achieves the best performance across all benchmarks, with up to 10% improvement in mean accuracy. Dataset Method NoiseBlurWeatherDigital Mean Gauss. Shot Impul. Defoc. Glass Motion Zoom Snow Frost Fog Brit. Contr. Elast. Pixel. JPEG CIFAR10-C Source36.0 40.0 43.570.141.464.369.8 70.8 72.6 66.6 81.3 64.659.3 48.6 56.9 59.3 TDA41.8 43.2 41.771.344.766.972.4 72.6 74.7 68.4 83.5 66.162.9 50.9 55.8 61.1 DMN38.9 39.3 42.570.639.265.172.7 72.3 73.4 66.4 82.8 58.660.7 49.1 56.3 59.1 VTE47.7 49.8 53.671.654.267.972.9 76.976.5 70.9 83.7 60.969.258.7 61.2 65.3 ZERO36.9 41.6 46.870.842.165.371.7 71.9 73.4 68.8 83.0 65.362.4 47.7 59.0 60.4 ECALP44.4 47.3 44.270.843.267.974.2 72.7 74.7 67.7 82.2 62.961.5 47.7 55.8 60.9 RoTTA36.7 41.1 43.770.242.864.770.0 71.2 72.6 66.9 81.8 64.760.3 49.1 57.3 59.1 TPT43.6 46.8 48.071.147.866.572.0 73.5 76.4 68.6 84.0 66.464.1 51.4 58.1 62.4 MEMO36.7 40.6 44.171.242.364.770.2 72.1 73.4 68.1 82.2 64.461.0 47.5 57.4 59.6 WATT43.6 49.1 49.472.146.467.071.4 73.9 74.1 71.2 83.9 72.861.6 58.8 63.263.6 MINT54.457.847.573.355.974.076.174.5 74.6 70.5 85.6 70.964.5 59.259.4 66.4 BATCLIP 51.8 56.0 54.2 76.055.274.675.5 76.8 78.575.286.377.067.1 57.8 61.6 68.2 Ours68.0 72.1 65.481.370.281.183.4 83.1 83.5 84.2 88.4 86.374.5 80.3 73.3 78.2 CIFAR100-C Source15.8 18.1 17.339.317.438.243.5 42.2 43.3 39.6 50.8 29.529.2 23.3 29.6 31.5 TDA18.7 20.9 19.840.217.939.745.1 44.3 45.2 40.3 52.2 30.929.6 23.0 31.0 33.7 DMN17.3 20.0 13.736.915.640.645.6 43.2 43.9 39.5 52.1 27.227.5 19.5 29.2 31.7 VTE16.7 18.1 19.140.022.938.743.7 45.0 45.2 39.0 49.8 28.634.4 27.1 30.2 33.4 ZERO15.5 18.2 19.741.317.240.044.3 43.4 43.4 40.8 51.4 29.330.4 21.5 31.5 32.2 ECALP18.7 19.2 17.438.317.839.944.3 43.7 44.9 41.0 52.7 31.230.7 23.1 30.1 33.2 RoTTA16.4 18.8 18.238.717.639.043.3 42.8 43.8 39.7 51.0 29.029.1 23.7 30.2 32.2 TPT16.5 17.5 17.039.119.338.843.9 43.4 44.8 40.3 50.7 27.630.5 23.8 29.3 32.4 MEMO16.9 18.1 18.141.317.240.645.5 44.3 44.4 40.5 52.6 29.730.9 22.6 31.3 33.1 WATT21.7 22.0 23.747.818.344.349.947.747.545.257.1 44.132.8 29.935.338.2 MINT23.726.321.546.023.542.348.5 46.5 45.2 43.3 55.7 38.633.8 28.2 32.1 37.2 BATCLIP 21.5 25.0 22.646.622.944.449.5 47.0 46.5 44.7 58.138.634.628.6 33.4 37.3 Ours32.7 35.4 30.749.834.948.653.2 50.2 50.9 50.0 58.8 49.641.2 41.5 39.8 44.2 ImageNet-C Source13.2 13.1 12.424.511.423.120.6 25.3 26.3 30.5 50.9 17.019.1 32.1 29.5 23.2 TDA12.4 15.0 14.924.013.323.421.0 26.9 27.832.7 51.8 18.520.3 33.4 30.6 24.6 DMN13.5 14.1 14.723.312.021.819.4 23.4 26.1 29.3 50.7 14.820.3 32.1 29.4 23.3 VTE11.9 12.0 13.624.611.522.922.4 27.0 26.7 32.1 51.317.219.9 35.3 33.0 24.5 ZERO11.9 13.0 12.724.911.822.521.8 26.5 26.9 31.0 51.1 16.719.5 34.1 30.2 23.3 ECALP14.2 15.5 15.023.112.623.321.0 24.1 25.4 29.7 48.4 18.019.4 31.3 28.9 23.1 RoTTA13.5 13.7 13.524.212.523.020.0 25.5 26.4 30.2 50.0 17.619.4 32.1 29.5 23.5 TPT12.5 12.3 12.625.012.122.920.7 26.8 26.6 30.1 50.9 16.919.9 33.1 30.1 24.0 MEMO12.4 13.4 13.124.911.522.720.1 25.4 25.8 30.3 50.1 17.519.0 32.1 29.0 23.5 WATT14.5 14.2 14.226.1 15.525.322.3 26.4 25.4 31.2 50.3 22.619.4 33.1 30.3 24.7 MINT18.719.519.824.718.827.522.8 27.6 27.6 32.4 50.9 20.623.6 34.7 33.4 26.8 BATCLIP 17.6 18.8 16.824.920.528.024.329.127.4 35.749.4 20.228.035.734.5 27.5 Ours23.5 24.5 24.127.525.430.127.9 31.3 30.3 37.2 45.7 27.831.9 36.0 34.030.6 D Limitations & Future Works While ORIGIN demonstrates strong performance, we acknowledge a few limitations. Firstly, ORIGIN is an on line VLM TTA method which is not directly applicable to strictly episodic TTA settings without maintaining an explicit memory for historical samples. Secondly, like most training- based VLM TTA methods, ORIGIN requires access to model gradients for adapting VLMs at test 14 time, which may limits its applicability to closed-source proprietary models. For future works, it would be interesting to discover episodic extension of ORIGIN by leveraging efficient OT variants, e.g., sliced OT [Tanguy et al., 2025], for incremental updates of the transport plan, or extending the OT framework to black-box adaption settings. E Boarder Impact This paper aim to advance the field of cross-modal learning, vision-language model, and optimal transport. 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