ICLR 2026 Papers

Category-agnostic pose estimation (CAPE) aims to localize keypoints on query images from arbitrary categories, using only a few annotated support examples for guidance. Recent approaches either treat keypoints as isolated entities or rely on manually defined skeleton priors, which are costly to annotate and inherently inflexible across diverse categories. Such oversimplification limits the model’s capacity to capture instance-wise structural cues critical for accurate pixel-level localization. To overcome these limitations, we propose \textbf{GenCape}, a \textbf{Gen}erative-based framework for \textbf{CAPE} that infers keypoint relationships solely from image-based support inputs, without additional textual descriptions or predefined skeletons. Our framework consists of two principal components: an iterative Structure-aware Variational Autoencoder (i-SVAE) and a Compositional Graph Transfer (CGT) module. The former infers soft, instance-specific adjacency matrices from support features through variational inference, embedded layer-wise into the Graph Transformer Decoder for progressive structural priors refinement. The latter adaptively aggregates multiple latent graphs into a query-aware structure via Bayesian fusion and attention-based reweighting, enhancing resilience to visual uncertainty and support-induced bias. This structure-aware design facilitates effective message propagation among keypoints and promotes semantic alignment across object categories with diverse keypoint topologies. Experimental results on the MP-100 dataset show that our method achieves substantial gains over graph-support baselines under both 1- and 5-shot settings, while maintaining competitive performance against text-support counterparts.

Simultaneously achieving robust classification and high-fidelity generative modeling within a single framework presents a significant challenge. Hybrid approaches, such as Joint Energy-Based Models (JEM), interpret classifiers as EBMs but are often limited by the instability and poor sample quality inherent in training based on Stochastic Gradient Langevin Dynamics (SGLD). We address these limitations by proposing a novel training framework that integrates adversarial training (AT) principles for both discriminative robustness and stable generative learning. The proposed method introduces three key innovations: (1) the replacement of SGLD-based JEM learning with a stable, AT-based approach that optimizes the energy function through a Binary Cross-Entropy (BCE) loss that discriminates between real data and contrastive samples generated via Projected Gradient Descent (PGD); (2) adversarial training for the discriminative component that enhances classification robustness while implicitly providing the gradient regularization needed for stable EBM training; and (3) a two-stage training strategy that addresses normalization-related instabilities and enables leveraging pretrained robust classifiers, generalizing effectively across diverse architectures. Experiments on CIFAR-10/100 and ImageNet demonstrate that our approach: (1) is the first EBM-based hybrid to scale to high-resolution datasets with high training stability, simultaneously achieving state-of-the-art discriminative and generative performance on ImageNet 256$\times$256; (2) uniquely combines generative quality with adversarial robustness, enabling faithful counterfactual explanations; and (3) functions as a competitive standalone generative model, matching the generative quality of autoregressive methods (VAR-d16) and surpassing diffusion models while offering unique versatility. Code is available at https://github.com/xuwangyin/DAT.

Predictive coding (PC) is an influential computational model of visual learning and inference in the brain. Classical PC was proposed as a top-down generative model, where the brain actively predicts upcoming visual inputs, and inference minimises the prediction errors. Recent studies have also shown that PC can be formulated as a discriminative model, where sensory inputs predict neural activities in a feedforward manner. However, experimental evidence suggests that the brain employs both generative and discriminative inference, while unidirectional PC models show degraded performance in tasks requiring bidirectional processing. In this work, we propose bidirectional PC (bPC), a PC model that incorporates both generative and discriminative inference while maintaining a biologically plausible circuit implementation. We show that bPC matches or outperforms unidirectional models in their specialised generative or discriminative tasks, by developing an energy landscape that simultaneously suits both tasks. We also demonstrate bPC's superior performance in two biologically relevant tasks including multimodal learning and inference with missing information, suggesting that bPC resembles biological visual inference more closely.

Diffusion-based image generative models produce high-fidelity images through iterative denoising but remain vulnerable to memorization, where they unintentionally reproduce exact copies or parts of training images. Recent memorization detection methods are primarily based on the norm of score difference as indicators of memorization. We prove that such norm-based metrics are mainly effective under the assumption of isotropic log-probability distributions, which generally holds at high or medium noise levels. In contrast, analyzing the anisotropic regime reveals that memorized samples exhibit strong angular alignment between the guidance vector and unconditional scores in the low-noise setting. Through these insights, we develop a memorization detection metric by integrating isotropic norm and anisotropic alignment. Our detection metric can be computed directly on pure noise inputs via two conditional and unconditional forward passes, eliminating the need for costly denoising steps. Detection experiments on Stable Diffusion v1.4 and v2 show that our metric outperforms existing denoising-free detection methods while being at least approximately 5x faster than the previous best approach. Finally, we demonstrate the effectiveness of our approach by utilizing a mitigation strategy that adapts memorized prompts based on our developed metric. The code is available at https://github.com/rohanasthana/memorization-anisotropy.

As generative models become ubiquitous, there is a critical need for fine-grained control over the generation process. Yet, while controlled generation methods from prompting to fine-tuning proliferate, a fundamental question remains unanswered: are these models truly controllable in the first place? In this work, we provide a theoretical framework to formally answer this question. Framing human-model interaction as a control process, we propose a novel algorithm to estimate the controllable sets of models in a dialogue setting. Notably, we provide formal guarantees on the estimation error as a function of sample complexity: we derive probably-approximately correct bounds for controllable set estimates that are distribution-free, employ no assumptions except for output boundedness, and work for any black-box nonlinear control system (i.e., any generative model). We empirically demonstrate the theoretical framework on different tasks in controlling dialogue processes, for both language models and text-to-image generation. Our results show that model controllability is surprisingly fragile and highly dependent on the experimental setting. This highlights the need for rigorous controllability analysis, shifting the focus from simply attempting control to first understanding its fundamental limits.

Recent work shows Tree-Sliced Optimal Transport to be an efficient and more expressive alternative to Sliced Wasserstein (SW), improving downstream performance. Tree-sliced metrics compare probability distributions by projecting measures onto tree metric spaces; a central example is the Tree-Sliced Wasserstein (TSW) distance, which applies the $1$-Wasserstein metric after projection. However, computing tree-based $p$-Wasserstein for general $p$ is costly, largely confining practical use to $p=1$. This restriction is a significant bottleneck, as higher-order metrics ($p > 1$) are preferred in gradient-based learning for their more favorable optimization landscapes. In this work, we revisit Sobolev integral probability metrics (IPM) on trees to obtain a practical generalization of TSW. Building on the insight that a suitably regularized Sobolev IPM admits a closed-form expression, we introduce TS-Sobolev, a tree-sliced metric that aggregates regularized Sobolev IPMs over random tree systems and remains tractable for all $p\ge1$; for $p>1$, TS-Sobolev has the same computational complexity as TSW at $p=1$. Notably, at $p=1$ it recovers TSW exactly. Consequently, TS-Sobolev serves as a drop-in replacement for TSW in practical applications, with an additional flexibility in changing $p$. Furthermore, we extend this framework to define a corresponding metric for probability measures on hyperspheres. Experiments on Euclidean and spherical datasets show that TS-Sobolev and its spherical variant improve downstream performance in gradient flows, self-supervised learning, generative modeling, and text topic modeling over recent SW and TSW variants.

Watermarking is a principled approach for tracing the provenance of large language model (LLM) outputs, but its deployment in practice is hindered by inference inefficiency. Speculative sampling accelerates inference, with efficiency improving as the acceptance rate between draft and target models increases. Yet recent work reveals a fundamental trade-off: higher watermark strength reduces acceptance, preventing their simultaneous achievement. We revisit this trade-off and show it is not absolute. We introduce a quantitative measure of watermark strength that governs statistical detectability and is maximized when tokens are deterministic functions of pseudorandom numbers. Using this measure, we fully characterize the trade-off as a constrained optimization problem and derive explicit Pareto curves for two existing watermarking schemes. Finally, we introduce a principled mechanism that injects pseudorandomness into draft-token acceptance, ensuring maximal watermark strength while maintaining speculative sampling efficiency. Experiments further show that this approach improves detectability without sacrificing efficiency. Our findings uncover a principle that unites speculative sampling and watermarking, paving the way for their efficient and practical deployment.

Large language models excel at reasoning but lack key aspects of introspection, including the ability to anticipate their own success and the computation required to achieve it. Humans use real-time introspection to decide how much effort to invest, when to make multiple attempts, when to stop, and when to signal success or failure. Without this ability, LLMs struggle to make intelligent meta-cognition decisions. Test-time scaling methods such as Best-of-N drive up cost and latency by using a fixed budget of samples regardless of the marginal benefit of each one at any point in generation, and the absence of confidence signals can mislead people, prevent appropriate escalation to better tools, and undermine trustworthiness. Learned verifiers or reward models can provide confidence estimates, but do not enable adaptive inference and add substantial inference cost by requiring extra models or forward passes. We present ZIP-RC, an adaptive inference method that equips models with zero-overhead inference-time predictions of reward and cost. At every token during generation, ZIP-RC reuses reserved or unused logits in the same forward pass as next-token prediction to output a joint distribution over final reward and remaining length—no extra models, architecture change, or inference overhead. This full joint distribution is used to compute a sampling utility which is the linear combination of the expected maximum reward, total compute, and latency of set of samples if generated to completion. During inference, we maximize this utility with meta-actions that determine which prefix of tokens to continue or initiate sampling from. On mixed-difficulty mathematical benchmarks, ZIP-RC improves accuracy by up to 12% over majority voting at equal or lower average cost, and traces smooth Pareto frontiers between quality, compute, and latency. By providing real-time reward–cost introspection, ZIP-RC allows models to reason adaptively and more efficiently.

Many generative models originally developed in finite-dimensional Euclidean space have functional generalizations in infinite-dimensional settings. However, the extension of rectified flow to infinite-dimensional spaces remains unexplored. In this work, we establish a rigorous functional formulation of rectified flow in an infinite-dimensional Hilbert space. Our approach builds upon the superposition principle for continuity equations in an infinite-dimensional space. We further show that this framework extends naturally to functional flow matching and functional probability flow ODEs, interpreting them as nonlinear generalizations of rectified flow. Notably, our extension to functional flow matching removes the restrictive measure-theoretic assumptions in the existing theory of \citet{kerrigan2024functional}. Furthermore, we demonstrate experimentally that our method achieves superior performance compared to existing functional generative models.

Decision-focused learning (DFL) integrates predictive models with downstream optimization, directly training machine learning models to minimize decision errors. While DFL has been shown to provide substantial advantages when compared to a counterpart that treats the predictive and prescriptive models separately, it has also been shown to struggle in high-dimensional and risk-sensitive settings, limiting its applicability in real-world settings. To address this limitation, this paper introduces Decision-Focused Generative Learning (Gen-DFL), a novel framework that leverages generative models to adaptively model uncertainty and improve decision quality. Instead of relying on fixed uncertainty sets, Gen-DFL learns a structured representation of the optimization parameters and samples from the tail regions of the learned distribution to enhance robustness against worst-case scenarios. This approach mitigates over-conservatism while capturing complex dependencies in the parameter space. The paper shows, theoretically, that Gen-DFL achieves improved worst-case performance bounds compared to traditional DFL. Empirically, it evaluates Gen-DFL on various scheduling and logistics problems, demonstrating its strong performance against existing DFL methods.

Recent progress in image-to-video (I2V) diffusion models has significantly advanced the field of generative inbetweening, which aims to generate semantically plausible frames between two keyframes. In particular, inference-time sampling strategies, which leverage the generative priors of large-scale pre-trained I2V models without additional training, have become increasingly popular. However, existing inference-time sampling, either fusing forward and backward paths in parallel or alternating them sequentially, often suffers from temporal discontinuities and undesirable visual artifacts due to the misalignment between the two generated paths. This is because each path follows the motion prior induced by its own conditioning frame. In this work, we propose Motion Prior Distillation (MPD), a simple yet effective inference-time distillation technique that suppresses bidirectional mismatch by distilling the motion residual of the forward path into the backward path. Our method can deliberately avoid denoising the end-conditioned path which causes the ambiguity of the path, and yield more temporally coherent inbetweening results with the forward motion prior. We not only perform quantitative evaluations on standard benchmarks, but also conduct extensive user studies to demonstrate the effectiveness of our approach in practical scenarios.

Probabilistic forecasting of multivariate time series is challenging due to non-stationarity, inter-variable dependencies, and distribution shifts. While recent diffusion and flow matching models have shown promise, they often ignore informative priors such as conditional means and covariances. In this work, we propose Conditionally Whitened Generative Models (CW-Gen), a framework that incorporates prior information through conditional whitening. Theoretically, we establish sufficient conditions under which replacing the traditional terminal distribution of diffusion models, namely the standard multivariate normal, with a multivariate normal distribution parameterized by estimators of the conditional mean and covariance improves sample quality. Guided by this analysis, we design a novel Joint Mean-Covariance Estimator (JMCE) that simultaneously learns the conditional mean and sliding-window covariance. Building on JMCE, we introduce Conditionally Whitened Diffusion Models (CW-Diff) and extend them to Conditionally Whitened Flow Matching (CW-Flow). Experiments on five real-world datasets with six state-of-the-art generative models demonstrate that CW-Gen consistently enhances predictive performance, capturing non-stationary dynamics and inter-variable correlations more effectively than prior-free approaches. Empirical results further demonstrate that CW-Gen can effectively mitigate the effects of distribution shift.

Electrostatic field matching (EFM) has recently appeared as a novel physics-inspired paradigm for data generation and transfer using the idea of an electric capacitor. However, it requires modeling electrostatic fields using neural networks, which is non-trivial because of the necessity to take into account the complex field outside the capacitor plates. In this paper, we propose Interaction Field Matching (IFM), a generalization of EFM which allows using general interaction fields beyond the electrostatic one. Furthermore, inspired by strong interactions between quarks and antiquarks in physics, we design a particular interaction field realization which solves the problems which arise when modeling electrostatic fields in EFM. We show the performance on a series of toy and image data transfer problems.

We present a general strategy for turning generative models into candidate solution samplers for batch Bayesian optimization (BO). The use of generative models for BO enables: large batch scaling as generative sampling, optimization of non-continuous design spaces, and high-dimensional and combinatorial design by using generative priors over feasible regions. Inspired by the success of direct preference optimization (DPO) and its variants, we show that its approach of directly training generative models using preferential rewards without the need for an intermediate reward model is extensible to the BO case. Furthermore, this framework is generalizable beyond preference-based feedback to general types of reward signals and loss functions. In essence, one can train a generative model with noisy, simple utility values directly computed from observations to then form proposal distributions whose densities are proportional to the expected utility, i.e., BO's acquisition function values. This perspective unifies recent progress in using generative models for black-box optimization and connects it with batch Bayesian optimization under a general framework. As theoretical results, we show that the generative models within the BO process approximately follow a sequence of distributions which asymptotically concentrate at the global optima under certain conditions. We also demonstrate this effect through experiments on challenging optimization problems involving large batches in high dimensions.

Anomaly detection refers to the techniques that identify (probably unseen) rare or suspicious data that deviate significantly from the pre-defined normal data (Chalapathy & Chawla, 2019; Ruff et al., 2021). Empirical studies have observed that generative models trained on normal data tend to produce larger reconstruction errors when reconstructing anomalies. Based on this observation, researchers have developed various anomaly detection methods, referred to as reconstruction-based anomaly detection (RBAD) (Lv et al., 2024; Li et al., 2024) in the literature. Despite the empirical success of RBAD, the theoretical understanding of RBAD is still limited. This paper provides a theoretical analysis of RBAD. We analyze the training dynamics of a 2-layer convolutional autoencoder and introduce the cone set of the features. We prove that the cone sets of the normal features would absorb the (convolutional) kernels of the autoencoder during training and use these absorbed kernels to reconstruct the inputs. The absorbed kernels are more aligned with the normal features, which explains the cause of the reconstruction error gap between the normal data and the anomalies. Synthesized experiments are provided to validate our theoretical findings. We also visualize the training dynamics of the autoencoder on real-world data, demonstrating our proposed cone set intuition.

Diffusion Transformers have achieved state-of-the-art performance in class-conditional and multimodal generation, yet the structure of their learned conditional embeddings remains poorly understood. In this work, we present the first systematic study of these embeddings and uncover a notable redundancy: class-conditioned embeddings exhibit extreme angular similarity, exceeding 99% on ImageNet-1K, while continuous-condition tasks such as pose-guided image generation and video-to-audio generation reach over 99.9%. We further find that semantic information is concentrated in a small subset of dimensions, with head dimensions carrying the dominant signal and tail dimensions contributing minimally. By pruning low-magnitude dimensions--removing up to two-thirds of the embedding space--we show that generation quality and fidelity remain largely unaffected, and in some cases improve. These results reveal a semantic bottleneck in Transformer-based diffusion models, providing new insights into how semantics are encoded and suggesting opportunities for more efficient conditioning mechanisms.

Generative foundation models (GenFMs), such as large language models and text-to-image systems, have demonstrated remarkable capabilities in various downstream applications. As they are increasingly deployed in high-stakes applications, assessing their trustworthiness has become both a critical necessity and a substantial challenge. Existing evaluation efforts are fragmented, rapidly outdated, and often lack extensibility across modalities. This raises a fundamental question: how can we systematically, reliably, and continuously assess the trustworthiness of rapidly advancing GenFMs across diverse modalities and use cases? To address these gaps, we introduce TrustGen, a dynamic and modular benchmarking system designed to systematically evaluate the trustworthiness of GenFMs across text-to-image, large language, and vision-language modalities. TrustGen standardizes trust evaluation through a unified taxonomy of over 25 fine-grained dimensions—including truthfulness, safety, fairness, robustness, privacy, and machine ethics—while supporting dynamic data generation and adaptive evaluation through three core modules: Metadata Curator, Test Case Builder, and Contextual Variator. Taking TrustGen into action to evaluate the trustworthiness of 39 models reveals four key insights. (1) State-of-the-art GenFMs achieve promising overall trust performance, yet significant limitations remain in specific dimensions such as hallucination resistance, fairness, and privacy preservation. (2) Contrary to prevailing assumptions, open-source models now rival and occasionally surpass proprietary systems in trustworthiness metrics. (3) The trust gap among top-performing models is narrowing, likely due to increased industry convergence on best practices. (4) Trustworthiness is not an isolated property; it interacts complexly with other behaviors, such as helpfulness and ethical decision-making. TrustGen is a transformative step toward standardized, scalable, and actionable trustworthiness evaluation, supporting dynamic assessments across diverse modalities and trust dimensions that evolve alongside the generative AI landscape.

Reinforcement learning (RL) has become a cornerstone for enhancing the reasoning capabilities of large language models (LLMs), with recent innovations such as Group Relative Policy Optimization (GRPO) demonstrating exceptional effectiveness. In this study, we identify a critical yet underexplored issue in RL training: low-probability tokens disproportionately influence model updates due to their large gradient magnitudes. This dominance hinders the effective learning of high-probability tokens, whose gradients are essential for LLMs' performance but are substantially suppressed. To mitigate this interference, we propose two novel methods: Advantage Reweighting and Low-Probability Token Isolation (Lopti), both of which effectively attenuate gradients from low-probability tokens while emphasizing parameter updates driven by high-probability tokens. Our approaches promote balanced updates across tokens with varying probabilities, thereby enhancing the efficiency of RL training. Experimental results demonstrate that they substantially improve the performance of GRPO-trained LLMs, achieving up to a 46.2% improvement in K&K Logic Puzzle reasoning tasks.

Neural network-based optimal transport (OT) is a recent and fruitful direction in the generative modeling community. It finds its applications in various fields such as domain translation, image super-resolution, computational biology and others. Among the existing OT approaches, of considerable interest are adversarial minimax solvers based on semi-dual formulations of OT problems. While promising, these methods lack theoretical investigation from a statistical learning perspective. Our work fills this gap by establishing upper bounds on the generalization error of an approximate OT map recovered by the minimax quadratic OT solver. Importantly, the bounds we derive depend solely on some standard statistical and mathematical properties of the considered functional classes (neural nets). While our analysis focuses on the quadratic OT, we believe that similar bounds could be derived for general OT case, paving the promising direction for future research. Our experimental illustrations are available online https://github.com/milenagazdieva/StatOT.