ICLR 2026 Papers

Diffusion bridge models have recently become a powerful tool in the field of generative modeling. In this work, we leverage their power to address another important problem in machine learning and information theory, the estimation of the mutual information (MI) between two random variables. Neatly framing MI estimation as a domain transfer problem, we construct an unbiased estimator for data posing difficulties for conventional MI estimators. We showcase the performance of our estimator on three standard MI estimation benchmarks, i.e., low-dimensional, image-based and high MI, and on real-world data, i.e., protein language model embeddings.

Representation alignment helps generation by distilling representations from a pretrained vision encoder to intermediate diffusion features. We investigate a fundamental question - `what aspect of the target representation matters for generation, its global information (measured by Imagenet1K accuracy) or its spatial structure (pairwise cosine similarity between patch tokens)''? Prevalent wisdom holds that stronger global performance leads to better generation as a target representation. To study this, we first perform a large-scale empirical analysis across 27 different vision encoders and different model scales. The results are surprising - spatial structure, rather than global performance drives the generation performance of a target representation. To further study this, we introduce two straightforward modifications, which specifically accentuate the transfer of spatial information. We replace the standard MLP projection layer in REPA with a simple convolution layer and introduce a spatial normalization layer for the external representation. Surprisingly, our simple method (implemented in <4 lines of code), termed iREPA, consistently improves convergence speed of REPA, across a diverse set of vision encoders, model sizes, and training variants (such as REPA-E and meanflow with REPA). Our work motivates revisiting the fundamental working mechanism of representational alignment and how it can be leveraged for improved training of generative models.

The ability of modern language models to easily extract unstructured sensitive information has made redaction—the selective removal of such information—an essential task for data security. However, existing benchmarks and evaluation methods for redaction are often limited to predefined categories of data like personally identifiable information (PII), or particular techniques like masking. To bridge this gap, we introduce RedacBench, a novel benchmark for a comprehensive evaluation of redaction capabilities, independent of specific domains or redaction strategies. Constructed from 514 human-written texts from individuals, corporations, and governments, along with 187 security policies, RedacBench measures a model's ability to selectively remove policy-violating information while preserving the original text's utility. We robustly quantify this performance using metrics derived from 8,053 inferable propositions, assessing both security—through the redaction of sensitive propositions—and utility—through the preservation of non-sensitive ones. Our experiments on various redaction strategies using state-of-the-art language models reveal that while more advanced models and strategies can increase security, maintaining utility remains a significant challenge. To facilitate future research, we publicly release RedacBench along with a web-based playground for custom dataset creation and evaluation at https://redacbench.vercel.app/.

Many computer vision tasks share substantial overlapping information, yet conventional codecs tend to ignore this, leading to redundant and inefficient representations. The Gray-Wyner network, a classical concept from information theory, offers a principled framework for separating common and task-specific information. Inspired by this idea, we develop a learnable three-channel codec that disentangles shared information from task-specific details across multiple vision tasks. We characterize the limits of this approach through the notion of lossy common information, and propose an optimization objective that balances inherent tradeoffs in learning such representations. Through comparisons of three codec architectures on two-task scenarios spanning six vision benchmarks, we demonstrate that our approach substantially reduces redundancy and consistently outperforms independent coding. These results highlight the practical value of revisiting Gray-Wyner theory in modern machine learning contexts, bridging classic information theory with task-driven representation learning.

When compressing continuous data, some loss of information is inevitable, and this incurred a distortion when reconstruction the data. The Rate–Distortion (RD) function characterizes the minimum achievable rate for a code whose decoding permits a specified amount of distortion. We exploit the connection between rate-distortion theory and entropic optimal transport to propose a novel stochastic-control formulation for the former, and use a classic result dating back to Schrodinger to show that the tradeoff between rate and mean squared error distortion is equivalent to a tradeoff between control energy and the differential entropy of the terminal state, whose probability law defines the reconstruction distribution. For a special class of sources, we show that the optimal control law and the corresponding trajectory in the space of probability measures are obtained by solving a backward heat equation. In more general settings, our approach yields a numerical method that estimates the RD function using diffusion processes with a constant diffusion coefficient. We demonstrate the effectiveness of our method through several examples.

We study the problem of online learning in Stackelberg games with side information between a leader and a sequence of followers. In every round the leader observes contextual information and commits to a mixed strategy, after which the follower best-responds. We provide learning algorithms for the leader which achieve O(T^{1/2}) regret under bandit feedback, an improvement from the previously best-known rates of O(T^{2/3}). Our algorithms rely on a reduction to linear contextual bandits in the utility space: In each round, a linear contextual bandit algorithm recommends a utility vector, which our algorithm inverts to determine the leader's mixed strategy. We extend our algorithms to the setting in which the leader's utility function is unknown, and also apply it to the problems of bidding in second-price auctions with side information and online Bayesian persuasion with public and private states. Finally, we observe that our algorithms empirically outperform previous results on numerical simulations.

Brain tumor segmentation in multi-modal MRIs poses significant challenges when one or more modalities are missing. Recent approaches commonly employ parallel fusion strategies; however, these methods often risk losing crucial shared information across modalities, which can degrade segmentation performance. In this paper, we advocate leveraging sequential information bottleneck fusion to effectively preserve shared information across modalities. From an information-theoretic perspective, sequential fusion not only produces more robust fused representations in missing-data scenarios but also achieves a tighter generalization upper bound compared to parallel fusion approaches. Building on this principle, we propose the Sequential Multi-modal Segmentation Network (SMSN), which integrates an Information-Bottleneck Fusion Module (IBFM). The IBFM sequentially extracts modality-common features while reconstructing modality-specific features through a dedicated feature extraction module. Extensive experiments on the BRATS18 and BRATS20 glioma datasets demonstrate that SMSN consistently outperforms traditional parallel fusion-based baselines, achieving exceptional robustness in diverse missing-modality settings. Furthermore, SMSN exhibits superior cross-domain generalization, as evidenced by its ability to transfer a trained model from BRATS20 to a brain metastasis dataset without fine-tuning. To ensure reproducibility, the code of the SMSN is provided in the supplementary file.

Artificial Intelligence Generated Content (AIGC), particularly video generation with diffusion models, has been advanced rapidly. Invisible watermarking is a key technology for protecting AI-generated videos and tracing harmful content, and thus plays a crucial role in AI safety. Beyond post-processing watermarks which inevitably degrade video quality, recent studies have proposed distortion-free in-generation watermarking for video diffusion models. However, existing in-generation approaches are non-blind: they require maintaining all the message-key pairs and performing template-based matching during extraction, which incurs prohibitive computational costs at scale. Moreover, when applied to modern video diffusion models with causal 3D Variational Autoencoders (VAEs), their robustness against temporal disturbance becomes extremely weak. To overcome these challenges, we propose SIGMark, a Scalable In-Generation watermarking framework with blind extraction for video diffusion. To achieve blind-extraction, we propose to generate watermarked initial noise using a Global set of Frame-wise PseudoRandom Coding keys (GF-PRC), reducing the cost of storing large-scale information while preserving noise distribution and diversity for distortion-free watermarking. To enhance robustness, we further design a Segment Group-Ordering module (SGO) tailored to causal 3D VAEs, ensuring robust watermark inversion during extraction under temporal disturbance. Comprehensive experiments on modern diffusion models show that SIGMark achieves very high bit-accuracy during extraction under both temporal and spatial disturbances with minimal overhead, demonstrating its scalability and robustness.

Large Vision Language Models (LVLMs) have recently emerged as powerful architectures capable of understanding and reasoning over both visual and textual information. These models typically rely on two key components: a Vision Transformer (ViT) and a Large Language Model (LLM). ViT encodes visual content into a sequence of image tokens and serves as the perceptual front-end -- the eyes of the model. In contrast, the LLM interprets these tokens to perform high-level reasoning, generates responses, and functions as the cognitive core -- the brain of the model. However, it remains unclear which visual tokens contribute most significantly to understanding and reasoning, and how effectively these signals are propagated from ViT to the LLM. While most existing works have focused on identifying attention sinks, low-semantic tokens receiving disproportionately high attention, within the LLM, we shift the focus to the vision encoder by identifying a class of high-norm visual tokens from ViT, referred to as ViT attention sinks -- a problem that has been rarely studied but is indeed very important for LVLMs. Our findings show that these ViT sinks encapsulate high-level semantic concepts from images, allowing the LLM to perform more effective understanding and reasoning. Despite their importance, these sink tokens are often overlooked in existing LVLM architectures. To explore their contribution, we present both qualitative and quantitative analyses of the information embedded in these sink tokens. We also propose both training-free and training-based approaches to better leverage how this information is interpreted by the LLM, and to what extent. By explicitly utilizing these tokens, we demonstrate substantial improvements across a range of LVLMs and visual reasoning tasks, including but not limited to mathematical problem solving, logical inference, and geometric understanding, highlighting the untapped potential of ViT attention sinks in enhancing visual reasoning.

The training dynamics of deep neural networks often defy expectations, even as these models form the foundation of modern machine learning. Two prominent examples are grokking, where test performance improves abruptly long after the training loss has plateaued, and the information bottleneck principle, where models progressively discard input information irrelevant to the prediction task as training proceeds. However, the mechanisms underlying these phenomena and their relations remain poorly understood. In this work, we present a unified explanation of such late-phase phenomena through the lens of neural collapse, which characterizes the geometry of learned representations. We show that the contraction of population within-class variance is a key factor underlying both grokking and information bottleneck, and relate this measure to the neural collapse measure defined on the training set. By analyzing the dynamics of neural collapse, we show that distinct time scales between fitting the training set and the progression of neural collapse account for the behavior of the late-phase phenomena. Finally, we validate our theoretical findings on multiple datasets and architectures.

Incorporating robustness in generative modeling has enticed many researchers of the field. To this end, we introduce a new class of multivariate power-law distributions---the symmetric Pareto (symPareto) distribution---which can be viewed as an $\ell_1$-norm-based counterpart of the multivariate $t$ distribution. The symPareto distribution possesses many attractive information-geometric properties with respect to the $\gamma$-power divergence that naturally populates power-law families. Leveraging on the joint minimization view of variational inference, we propose the ParetoVAE, a probabilistic autoencoder that minimizes the $\gamma$-power divergence between two statistical manifolds. ParetoVAE employs the symPareto distribution for both prior and encoder, with flexible decoder options including Student's $t$ and symPareto distributions. Empirical evidences demonstrate ParetoVAE's effectiveness across multiple domains through varying the types of the decoder. The $t$ decoder achieves superior performance in sparse, heavy-tailed data reconstruction and word frequency analysis; the symPareto decoder enables robust high-dimensional denoising.

Multiple agents are increasingly combined to make decisions with the expectation of achieving complementary performance, where the decisions they make together outperform those made individually. However, knowing how to improve the performance of collaborating agents requires knowing what information and strategies each agent employs. With a focus on human-AI pairings, we contribute a decision-theoretic framework for characterizing the value of information. By defining complementary information, our approach identifies opportunities for agents to better exploit available information–in AI-assisted decision workflows. We present a novel explanation technique (ILIV-SHAP) that adapts SHAP explanations to highlight human-complementing information. We validate the effectiveness of the framework on examples from chest X-ray diagnosis and deepfake detection and ILIV-SHAP through a study of human-AI decision-making. We also find that presenting ILIV-SHAP with AI predictions leads to reliably greater reductions in error over non-AI assisted decisions more than vanilla SHAP.

Denoising diffusions sample from a probability distribution $\mu$ in $\mathbb{R}^d$ by constructing a stochastic process $(\hat{\mathbf{x}}_t:t\ge 0)$ in $\mathbb{R}^d$ such that $\hat{\mathbf{x}}_0$ is easy to sample, but the distribution of $\hat{\mathbf{x}}_T$ at large $T$ approximates $\mu$. The drift $\mathbf{m}:\mathbb{R}^{d}\times\mathbb{R}\to\mathbb{R}^d$ of this diffusion process is learned by minimizing a score-matching objective. Is every probability distribution $\mu$, for which sampling is tractable, also amenable to sampling via diffusions? We address this question by studying its relation to information-computation gaps in statistical estimation. Earlier work in this area constructs broad families of distributions $\mu$ for which sampling is easy, but approximating the drift $\mathbf{m}(\mathbf{y},t)$ is conjectured to be intractable, and provides rigorous evidence for intractability. We prove that this implies a failure of sampling via diffusions. First, there exist drifts whose score matching objective is superpolynomially close to the optimum value (among polynomial time drifts) and yet yield samples with distribution that is very far from the target one. Second, any polynomial-time drift that is also Lipschitz continuous results in equally incorrect sampling. We instantiate our results on the toy problem of sampling a sparse low-rank matrix, and further demonstrate empirically the failure of diffusion-based sampling. Our work implies that caution should be used in adopting diffusion sampling when other approaches are available.

We present a novel geometric perspective on the latent space of diffusion models. We first show that the standard pullback approach, utilizing the deterministic probability flow ODE decoder, is fundamentally flawed. It provably forces geodesics to decode as straight segments in data space, effectively ignoring any intrinsic data geometry beyond the ambient Euclidean space. Complementing this view, diffusion also admits a stochastic decoder via the reverse SDE, which enables an information geometric treatment with the Fisher-Rao metric. However, a choice of $\mathbf{x}_T$ as the latent representation collapses this metric due to memorylessness. We address this by introducing a latent spacetime $\mathbf{z}=(\mathbf{x}_t,t)$ that indexes the family of denoising distributions $p(\mathbf{x}_0 | \mathbf{x}_t)$ across all noise scales, yielding a nontrivial geometric structure. We prove these distributions form an exponential family and derive simulation-free estimators for curve lengths, enabling efficient geodesic computation. The resulting structure induces a principled Diffusion Edit Distance, where geodesics trace minimal sequences of noise and denoise edits between data. We also demonstrate benefits for transition path sampling in molecular systems, including constrained variants such as low-variance transitions and region avoidance. Code is available at: https://github.com/rafalkarczewski/spacetime-geometry.

Figuring out how neural language models comprehend syntax acts as a key to revealing how they understand languages. We systematically analyzed methods of extracting syntax from models, namely _probing_, and found limitations yet widely exist in previous probing practice. We proposed a method capable of estimating mutual information (MI) and directly extracting dependency trees from attention scores in a mathematical-rigorous way, requiring no additional network training effort. Compared with previous approaches, it has a much simpler model, while being able to probe more complex dependency trees, also transparent for fine-grained explanation. We tested our method on several open-source LLMs and demonstrated its effectiveness by systematically comparing it with a great many competitive baselines. Several informative conclusions can be drawn by further analysis of the results, shedding light on our method’s explanatory potential. An anonymous and off-the-shelf version of our code is released at https://anonymous.4open.science/r/IPBP-99F1.

Understanding how neural populations in higher visual areas encode object-centered visual information remains a central challenge in computational neuroscience. Prior works have investigated representational alignment between artificial neural networks and the visual cortex. Nevertheless, these findings are indirect and offer limited insights to the structure of neural populations themselves. Similarly, decoding-based methods have quantified semantic features from neural populations but have not uncovered their underlying organizations. This leaves open a scientific question: ``how feature-specific visual information is distributed across neural populations in higher visual areas, and whether it is organized into structured, semantically meaningful subspaces" To tackle this problem, we present MIG-Vis, a method that leverages the generative power of diffusion models to visualize and validate the visual-semantic attributes encoded in neural latent subspaces. Our method first uses a variational autoencoder to infer a **group-wise disentangled** neural latent subspace from neural populations. Subsequently, we propose a **mutual information** (MI)–guided diffusion synthesis procedure to visualize the specific visual-semantic features encoded by each latent group. We validate MIG-Vis on multi-session neural spiking datasets from the inferior temporal (IT) cortex of two macaques. The synthesized results demonstrate that our method identifies neural latent groups with clear semantic selectivity to diverse visual features, including object pose, inter-category transformations, and intra-class content. These findings provide direct, interpretable evidence of structured semantic representation in the higher visual cortex and advance our understanding of its encoding principles.

Sensory representation is typically understood through a hierarchical-causal framework where progressively abstract features are extracted sequentially. However, this causal view fails to explain misrepresentation, a phenomenon better handled by an informational and teleological view based on decodable content and downstream functions. This creates a tension: how does a system that abstracts away details preserve the fine-grained information needed for downstream functions? We propose readout representation to resolve this, defining representation by the information recoverable from features, rather than their causal origin. Empirically, we show that inputs can be accurately reconstructed even from heavily perturbed mid-level features, demonstrating that a single input corresponds to a broad, redundant region of feature space, challenging the causal mapping perspective. To quantify this property, we introduce representation size, a metric linked to model robustness and representational redundancy. Our framework offers a new lens for analyzing how both biological and artificial neural systems learn complex features while maintaining robust, information-rich representations of the world.

We present DiffBED, a Bayesian experimental design (BED) approach that scales to problems with high-dimensional design spaces. Our key insight is that current BED approaches typically cannot be scaled to real high--dimensional design problems because of the need to specify a likelihood model that remains accurate throughout the design space. We show that without this, their design optimisation procedures exploit deficiencies in the likelihood and produce implausible designs. We overcome this issue by introducing a generative prior over feasible designs using a diffusion model. By guiding this diffusion model using principled information-theoretic experimental design objectives, we are then able to generate highly informative yet realistic designs at an unprecedented scale: while previous applications of BED have been restricted to design spaces with a handful of dimensions, we show that DiffBED can successful scale to designing high-resolution images.

We propose a simple yet novel data augmentation method for general data modalities based on energy-based modeling and principles from information geometry. Unlike most existing learning-based data augmentation methods, which rely on learning latent representations with generative models, our proposed framework enables an intuitive construction of a geometrically aware latent space that represents the structure of the data itself, supporting efficient and explicit encoding and decoding procedures. We then present and discuss how to design latent spaces that will subsequently control the augmentation with the proposed algorithm. Empirical results demonstrate that our data augmentation method achieves competitive performance in downstream tasks compared to other baselines, while offering fine-grained controllability that is lacking in the existing literature.