ICML 2026 Papers

Contrastive representation learning (CRL) underpins many modern foundation models. Despite recent theoretical progress, existing analyses suffer from several key limitations: (i) the statistical consistency of CRL remains poorly understood; (ii) available generalization bounds deteriorate as the number of negative samples increases, contradicting the empirical benefits of large negative sets; and (iii) the retrieval performance of CRL has received limited theoretical attention. In this paper, we develop a unified statistical learning theory for CRL. For downstream tasks, we evaluate retrieval quality using an AUC-type population criterion and show that the contrastive loss is *statistically consistent* with optimal ranking. We further establish a *calibration-style inequality* that quantitatively relates excess contrastive risk to excess retrieval suboptimality. For upstream training, we study both supervised and self-supervised contrastive objectives and derive generalization bounds of order $O(1/m + 1/\sqrt{n})$ and $O(1/\sqrt{m} + 1/\sqrt{n})$, respectively, where $m$ denotes the number of negative samples and $n$ the number of anchor points. These bounds not only explain the empirical advantages of large negative sets but also reveal an explicit trade-off between $m$ and $n$. Extensive experiments on large-scale vision--language models corroborate our theoretical predictions.

Template-free retrosynthesis methods treat the task as black-box sequence generation, limiting learning efficiency, while semi-template approaches rely on rigid reaction libraries that constrain generalization. We address this gap with a key insight: atom ordering in neural representations matters. Building on this insight, we propose a structure-aware template-free framework that encodes the two-stage nature of chemical reactions as a positional inductive bias. By placing reaction center atoms at the sequence head, our method transforms implicit chemical knowledge into explicit positional patterns that the model can readily capture. The proposed RetroDiT backbone, a graph transformer with rotary position embeddings, exploits this ordering to prioritize chemically critical regions. Combined with discrete flow matching, our approach decouples training from sampling and enables generation in 20--50 steps versus 500 for prior diffusion methods. Our method achieves state-of-the-art performance on both USPTO-50k (61.2\% top-1) and the large-scale USPTO-Full (51.3\% top-1) with predicted reaction centers. With oracle centers, performance reaches 71.1\% and 63.4\% respectively, surpassing foundation models trained on 10 billion reactions while using orders of magnitude less data. Ablation studies further reveal that structural priors outperform brute-force scaling: a 280K-parameter model with proper ordering matches a 65M-parameter model without it.

Reasoning-intensive retrieval is increasingly important for downstream applications, requiring more than lexical overlap or coarse semantic matching. While prior work mainly relies on Language Models (LMs) to synthesize reasoning-oriented supervision, we posit that it is already latent in LM-based retrievers but suppressed by contrastive overfitting. To elicit this latent reasoning, we introduce ElicitR, a retriever–LM framework with generative regularization that captures nuanced relationships among a query and its candidate documents beyond binary relevance. Concretely, alongside contrastive learning, we regularize the retriever by co-training a small LM on query–positive–negative batches. Next token prediction (NTP) for each text is conditioned on its prefix and the other in-batch texts, with cross-text conditioning weighted by retriever-computed similarities. Using MS MARCO as the only paired query-document supervision and a 135M LM for generative regularization with unlabeled raw-text initialization, ElicitR consistently improves BRIGHT by 16-29% relative across 0.1B–3B retriever scales while maintaining performance on BEIR. At 3B, ElicitR reaches an nDCG@10 of 23.1, substantially outperforming larger models trained with far more curated pairs and proprietary APIs. Further analyses show that ElicitR prevents overfitting, improves retrieval calibration, and remains robust to batch sizes, supporting its practicality.

Recent video generation models have revealed the emergence of Chain-of-Frame (CoF) reasoning, enabling frame-by-frame visual inference. With this capability, video models have been successfully applied to various visual tasks (*e.g.*, maze solving, visual puzzles). However, their potential to enhance text-to-image (T2I) generation remains largely unexplored due to the absence of a clearly defined visual reasoning starting point and interpretable intermediate states in the T2I generation process. To bridge this gap, we propose **CoF-T2I**, a model that integrates CoF reasoning into T2I generation via progressive visual refinement, where intermediate frames act as explicit reasoning steps and the final frame is taken as output. To establish such explicit generation process, we curate **CoF-Evol-Instruct**, a dataset of CoF trajectories that model the generation process from semantics to aesthetics. To further improve quality and avoid motion artifacts, we enable an independent encoding operation for each frame. Experiments show that CoF-T2I significantly outperforms the base video model and achieves competitive performance, reaching 0.86 on GenEval and 7.468 on Imagine-Bench. These results indicate the substantial promise of video models for advancing high-quality text-to-image generation.

Probabilistic super-resolution of high-dimensional spatial fields using diffusion models is often computationally prohibitive due to the cost of operating directly in pixel space. We propose PODiff, a structured conditional generative framework that performs diffusion in a fixed, variance-ordered Proper Orthogonal Decomposition (POD) coefficient space, exploiting the orthogonality of POD modes to impose an interpretable, variance-ordered latent geometry. This design enables efficient ensemble generation, preserves dominant spatial structure, and yields spatially interpretable, well-calibrated uncertainty at substantially lower computational cost. We evaluate PODiff on sea surface temperature downscaling over the West Australian coast and on a controlled advection--diffusion benchmark. PODiff achieves reconstruction accuracy comparable to pixel-space and learned-latent diffusion while using a substantially smaller structured latent space, requiring significantly less memory, and producing more reliable uncertainty estimates than deterministic and Monte Carlo Dropout baselines.

Estimating full-hand grasp pressure from egocentric video is critical for immersive VR and robotic manipulation, yet dense tactile sensing often relies on intrusive hardware. Existing vision-based methods predominantly rely on planar surfaces or fingertip contacts, failing to generalize to complex 3D object interactions. Therefore, we introduce EgoTactile, a benchmark pairing egocentric video with full-hand pressure supervision for diverse everyday objects, incorporating a bare-hand transfer subset to enable generalization to natural scenarios. Leveraging this benchmark, we first establish EgoPressureFormer as a discriminative baseline. Beyond this, to explicitly address the uncertainty in partial observations, we propose EgoPressureDiff, a conditional diffusion framework that adapts a large-scale pre-trained video diffusion backbone. By combining rich world knowledge priors with a Physically-Informed Feature Rectification layer to inject semantic constraints, our approach effectively hallucinates plausible contact patterns and resolves visual-physical ambiguities. Extensive experiments demonstrate that our method achieves superior performance on the benchmark and robust transferability to in-the-wild scenarios. Our project page is at https://egotactile.github.io/.

Diffusion posterior sampling conditions diffusion priors on measurements, but data-consistency updates are typically scaled by hand-tuned guidance weights and can destabilize sampling under stiff, operator-dependent curvature. We replace scalar guidance with a per-noise-level damped Gauss--Newton correction computed in diffusion-state coordinates. The correction pulls likelihood gradients back through the denoiser, uses a one-sided curvature model that avoids forward denoiser Jacobians, and applies diffusion-calibrated rank-one damping aligned with the denoiser residual. Each correction is solved with matrix-free GMRES using automatic differentiation, and sampling proceeds with a variance-preserving Langevin transition with a closed-form drift/noise split. On FFHQ and ImageNet across inverse problems, it achieves competitive PSNR/SSIM/LPIPS while running markedly faster than most of the compared baselines; on accelerated MRI reconstruction, it achieves the best PSNR/SSIM among the compared baselines. Code is available at https://github.com/Seunghyeok0715/CLAMP

Diffusion models can unintentionally memorize training samples, raising concerns about privacy and copyright. While recent methods can detect memorization, they often rely on global or model-specific signals and provide limited insight into where memorization appears within a generated image. We provide a geometric characterization of local memorization as a coordinate-wise variance collapse. However, such collapse can also arise from intrinsic data constraints rather than overfitting. To isolate overfitting-driven memorization, we propose curvature-difference methods that subtract the curvature of an underfitted baseline, either the unconditional model or a less-trained version of itself. We further derive a score-difference proxy that provides a geometric explanation for the widely used score-difference-based detection metric. Experiments on Stable Diffusion, evaluated against ground-truth memorization masks, show that our method outperforms the prior attention-based localization method. Code is available at \url{https://github.com/Gwangho99/mem-curv-diff}.

Efficiently routing queries to the optimal large language model (LLM) is crucial for optimizing the cost-performance trade-off in multi-model systems. However, most existing routers rely on single-model selection, making them susceptible to misrouting. In this work, we formulate LLM routing as the $\alpha$-VOR problem to minimize expected set size while controlling the misrouting risk, and propose a novel method -- RACER, extending base routers to output model sets that can be subsequently aggregated for improved output. In particular, RACER constructs nested model sets via augmented scoring and utilizes finite-sample concentration bounds to calibrate a threshold that allows for both variable set sizes and abstention. We theoretically prove that RACER achieves rigorous distribution-free risk control on unseen test data in a post-hoc and model-agnostic manner. Extensive experiments verify our theoretical guarantees and demonstrate that RACER consistently enhances downstream accuracy across a wide range of benchmarks.

Many real-world datasets contain hidden structure that cannot be detected by simple linear correlations between input features. For example, latent factors may influence the data in a coordinated way, even though their effect is invisible to covariance-based methods such as PCA. In practice, nonlinear neural networks often succeed in extracting such hidden structure in unsupervised and self-supervised learning. However, constructing a minimal high-dimensional model where this advantage can be rigorously analyzed has remained an open theoretical challenge. We introduce a tractable high-dimensional spiked model with two latent factors: one visible to covariance, and one statistically dependent yet uncorrelated, appearing only in higher-order moments. PCA and linear autoencoders fail to recover the latter, while a minimal nonlinear autoencoder provably extracts both. We analyze both the population risk, and empirical risk minimization. Our model also provides a tractable example where self-supervised test loss is poorly aligned with representation quality: nonlinear autoencoders recover latent structure that linear methods miss, even though their reconstruction loss is higher.

Transformers are arguably the preferred architecture for language generation. In this paper, inspired by continued fractions, we introduce a new function class for generative modeling. The architecture family implementing this function class is named CoFrGeNets - Continued Fraction Generative Networks. We design novel architectural components based on this function class that can replace Multi-head Attention and Feed-Forward Networks in Transformer blocks while requiring much fewer parameters. We derive custom gradient formulations to optimize the proposed components more accurately and efficiently than using standard PyTorch-based gradients. Our components are a plug-in replacement requiring little change in training or inference procedures that have already been put in place for Transformer-based models thus making our approach easy to incorporate in large industrial workflows. We experiment on two very different transformer architectures GPT2-xl (1.5B) and Llama3 (3.2B), where the former we pre-train on OpenWebText and GneissWeb, while the latter we pre-train on the docling data mix which consists of nine different datasets. Results show that the performance on downstream classification, Q\& A, reasoning and text understanding tasks of our models is competitive and sometimes even superior to the original models with two thirds to half the parameters and shorter pre-training time. We believe that future implementations customized to hardware will further bring out the true potential of our architectures.

Text-to-video (T2V) generation aims to synthesize videos with high visual quality and temporal consistency that are semantically aligned with input text. Reward-based post-training has emerged as a promising direction to improve the quality and semantic alignment of generated videos. However, recent methods either rely on large-scale human preference annotations or operate on misaligned embeddings from pre-trained vision-language models, leading to limited scalability or suboptimal supervision. We present PISCES, an annotation-free post-training algorithm that addresses these limitations via a novel Dual Optimal Transport (OT)-aligned Rewards module. To align reward signals with human judgment, PISCES uses OT to bridge text and video embeddings at both distributional and discrete token levels, enabling reward supervision to fulfill two objectives: (i) a Distributional OT-aligned Quality Reward that captures overall visual quality and temporal coherence; and (ii) a Discrete Token-level OT-aligned Semantic Reward that enforces semantic, spatio-temporal correspondence between text and video tokens. To our knowledge, PISCES is the first to improve annotation-free reward supervision in generative post-training through the lens of OT. Experiments on both short- and long-video generation show that PISCES outperforms both annotation-based and annotation-free methods on VBench across Quality and Semantic scores, with human preference studies further validating its effectiveness. We show that the Dual OT-aligned Rewards module is compatible with multiple optimization paradigms, including direct backpropagation and reinforcement learning fine-tuning.

Diffusion models (DMs) are a state-of-the-art generative method to approximately sample from an unknown distribution. Their training and evaluation primarily rely on an Evidence Lower Bound (ELBO), which relates the Kullback-Leibler (KL) divergence of model samples to the score matching loss along the path, which serves as a tractable surrogate. The difference between sample quality and the score matching loss produced by this bound leads to the score matching gap, which is known to be tight in the worst-case but not descriptive of sample quality in general. In this work, we provide a theoretical analysis of this gap, developing tighter bounds for three metrics: KL divergence, reverse KL divergence, and Wasserstein distance, effectively exploiting the regularity of the class of score estimators. Our results suggest that the quality of the score approximation has more impact on closing the score matching gap for low noise scales. To obtain these bounds, our key technical insight is to exploit the contraction properties of the backward processes. In particular, we rely on entropy flows, logarithmic Sobolev inequalities and reflection couplings, rigorously linking the ergodicity of the Langevin diffusion to the score matching gap problem.

In-Context Learning (ICL) in transformers acts as an online associative memory and is believed to underpin their high performance on complex sequence processing tasks. However, in gated linear attention models, this memory has a fixed capacity and is prone to interference, especially for long sequences. We propose Palimpsa, a self-attention model that views ICL as a continual learning problem that must address a stability-plasticity dilemma. Palimpsa uses Bayesian metaplasticity, where the plasticity of each attention state is tied to an importance state grounded by a prior distribution that captures accumulated knowledge. We demonstrate that various gated linear attention models emerge as specific architecture choices and posterior approximations, and that Mamba2 is a special case of Palimpsa where forgetting dominates. This theoretical link enables the transformation of any non-metaplastic model into a metaplastic one, significantly expanding its memory capacity. Our experiments show that Palimpsa consistently outperforms baselines on the Multi-Query Associative Recall (MQAR) benchmark and on Commonsense Reasoning tasks.

Existing diffusion models have made significant progress in generating realistic images. However, their direct adaptation to remote sensing imagery often disregards intrinsic physical laws. This oversight frequently leads to spectral distortion and radiometric inconsistency, severely limiting the scientific utility of generated data. To address this issue, this paper introduces AnyBand-Diff, a novel spectral-prior-guided diffusion framework tailored for robust spectral reconstruction. Specifically, we design a Masked Conditional Diffusion backbone integrated with a dual stochastic masking strategy, empowering the model to recover complete spectral information from arbitrary band subsets. Subsequently, to ensure radiometric fidelity, a Physics-Guided Sampling mechanism is proposed, leveraging gradients from a differentiable physical model to explicitly steer the denoising trajectory toward the manifold of physically plausible solutions. Furthermore, a Multi-Scale Physical Loss is formulated to enforce rigorous constraints across pixel, region, and global levels in a joint manner. Extensive experiments confirm the effectiveness of AnyBand-Diff in generating reliable imagery and achieving accurate spectral reconstruction, contributing to the advancement of physics-aware generative methods for Earth observation.

Guidance methods, such as classifier-free guidance (CFG) and auto-guidance (AG), have advanced noise-to-data generation in diffusion models. Recently, bridge models have introduced a data-to-data generative process that can exploit an instructive clean prior. In this work, inspired by previous methods creating quality difference between denoising results as guidance, we propose a training-free bridge guidance method, termed Prior Guidance (PG). Specifically, we introduce a weak prior, which is unseen during bridge pre-training, hindering prior exploitation and thereby degrading denoising result. Then, we contrast it with the seen prior to highlight and enhance prior exploitation via a scaling factor. Moreover, we analyze the underlying mechanism of prior exploitation in the bridge process and design frequency-modulated prior guidance (FMPG), which tailors the guidance scale to low- and high-frequency bands coherent with bridge generative dynamics. To address prior exploitation in image in-painting, we develop a cascaded framework, CFG-FMPG, which first generates a noisy hidden representation via CFG and then exploits it as a generative prior with FMPG, fulfilling their complementary strengths without compromising inference efficiency. Experiments demonstrate that our PG methods consistently improve pre-trained bridge models across diverse image translation tasks.

The unification of generative details and discriminative semantics presents a structural paradox in *diffusion-based representation learning*. Early approaches decouple semantics from generation, inevitably compromising representational completeness (i.e., *information split*). While recent bridge-based methods achieve unification via a tightly coupled mapping, they suffer from *information overload*. This is because unconstrained reconstruction objectives incentivize the encoder to entangle high-frequency stochastic noise into the latent bottleneck. To solve this, we introduce *asymmetric rectified contrastive diffusion autoencoder* (ArcDAE), which rebuilds the diffusion bridge as a *dynamic sifter*. Through imposing a *timestep-aware rectification constraint* that orthogonalizes the semantic manifold from the stochastic noise space, ArcDAE compels the bottleneck to distill discriminative features while actively shedding high-frequency redundancy. Consequently, our approach eliminates the overload trap without reverting to decoupling. Extensive experiments validate the superiority of our FFHQ-trained ArcDAE, surpassing state-of-the-art methods by up to 6.4% in downstream semantics regression and 9.7% in reconstruction fidelity.

Classifier-Free Guidance (CFG) is a cornerstone of flow-matching models, significantly enhancing visual quality and prompt adherence. However, high guidance scales inherently violate the optimal transport dynamics, leading to visual artifacts and mode collapse. In this paper, we investigate the mechanisms of this failure through the lens of velocity moment decomposition. Our analysis reveals that the distributional shift induced by CFG decouples into two geometric components: a Linear Barycentric Drift that shifts the global distribution center, and a Quadratic Energetic Instability that injects surplus kinetic energy, disrupting the transport cost and triggering variance explosion. To mitigate these issues, we introduce MIST (Moment-aligned Invariant Stability Transform), a training-free method designed to confine the sampling trajectory to the learned data manifold. MIST comprises two hierarchical stages: (1) Invariant Alignment (IA), a global statistical rectifier that restores structural integrity by removing the linear drift and realigning the energy profile; and (2) Stability Thresholding (ST), a local dynamical regulator that enforces Lipschitz-like smoothness via temporal decay and spatial suppression. MIST enables robust, high-fidelity generation across a wide range of guidance scales while consistently improving performance at moderate scales. Extensive experiments on diverse text-to-image and text-to-video benchmarks demonstrate that MIST outperforms standard CFG and state-of-the-art corrections, establishing a new benchmark for robust guidance in flow-based generative models.

Quadratic Discriminant Analysis (QDA) assumes Gaussian class-conditional distributions, causing systematic misclassification when data exhibit heavy tails. We propose Stable-QDA, which replaces the Gaussian likelihood with a symmetric $\alpha$-stable likelihood that decays polynomially rather than exponentially in Mahalanobis distance. Crucially, we find that correcting likelihood misspecification yields larger gains than robustifying parameter estimation: standard estimators (sample mean, Ledoit--Wolf covariance) often outperform robust alternatives when class heteroscedasticity is discriminative. We provide consistency guarantees under infinite-variance regimes, data-driven diagnostics for estimator selection, and demonstrate 15--53\% error reduction on real-world heavy-tailed benchmarks.