ICLR 2026 Papers

Standard autoregressive language models generate text token-by-token from a fixed vocabulary, inducing a *tree-structured state space* when viewing token sampling as an action, which limits flexibility and expressiveness. Recent work introduces dynamic vocabulary by sampling retrieved text spans but overlooks that the same sentence can be composed of spans of varying lengths, lacking explicit modeling of the *directed acyclic graph (DAG) state space*. This leads to restricted exploration of compositional paths and is biased toward the chosen path. Generative Flow Networks (GFlowNets) are powerful for efficient exploring and generalizing over state spaces, particularly those with a DAG structure. However, prior GFlowNets-based language models operate at the token level and remain confined to tree-structured spaces, limiting their potential. In this work, we propose **F**low **o**f **S**pan**S** (**FOSS**), a principled GFlowNets framework for span generation. FoSS constructs a dynamic span vocabulary by segmenting the retrieved text flexibly, ensuring a DAG-structured state space, which allows GFlowNets to explore diverse compositional paths and improve generalization. With specialized reward models, FoSS generates diverse, high-quality text. Empirically, FoSS improves MAUVE scores by up to 12.5\% over Transformer on text generation and achieves 3.5\% gains on knowledge-intensive tasks, consistently outperforming state-of-the-art methods. Scaling experiments further demonstrate FoSS benefits from larger models, more data, and richer retrieval corpora, retaining its advantage over strong baselines.

Prevailing methods for training Large Language Models (LLMs) as text encoders rely on contrastive losses that treat the model as a black-box function, discarding its generative and reasoning capabilities in favor of static embeddings. We introduce \GRACE{} (Generative Representation Learning via Contrastive Policy Optimization), a novel framework that reimagines contrastive signals not as losses to be minimized, but as rewards that guide a generative policy. In GRACE, the LLM acts as a policy $\pi_\theta$ that produces explicit, human-interpretable rationales—structured natural language explanations of its semantic understanding. These rationales are then encoded into high-quality embeddings via mean pooling. Using policy gradient optimization, we train the model with a multi-component reward function that maximizes similarity between query--positive pairs and minimizes similarity with negatives. This transforms the LLM from an opaque encoder into an interpretable agent whose reasoning process is transparent and inspectable. On MTEB benchmark, GRACE yields broad cross-category gains: averaged over four backbones, the supervised setting improves overall score by 11.5\% over base models, and the unsupervised variant adds 6.9\%, while preserving general capabilities. This work treats contrastive objectives as rewards over rationales, unifying representation learning with generation to produce stronger embeddings and transparent decision traces.

In arbitrary-order language models, it is an open question how to sample tokens in parallel from the correct joint distribution. With discrete diffusion models, the more tokens they generate in parallel, the less their predicted distributions adhere to the originally learned data distribution, as they rely on a conditional independence assumption that only works with infinitesimally small timesteps. We find that a different class of models, any-subset autoregressive models (AS-ARMs), holds the solution. As implied by the name, AS-ARMs can generate tokens in any order, and in parallel. Moreover, AS-ARMs support parallelized joint probability density estimation, allowing them to correct their own parallel-generated token distributions, via our Any-Subset Speculative Decoding (ASSD) algorithm. ASSD provably enables generation of tokens from the correct joint distribution, with the number of neural network calls upper bounded by the number of tokens predicted – notably, previous speculative decoding algorithms lack our efficiency guarantee. We empirically verify that ASSD speeds up language generation, without sacrificing quality. Furthermore, we provide a mathematically justified scheme for training AS-ARMs for generation, and show that AS-ARMs achieve state-of-the-art performance among sub-200M parameter models on infilling benchmark tasks, and nearly match the performance of models 50X larger on code generation. Our theoretical and empirical results indicate that the once-forgotten AS-ARMs are a promising direction of language modeling.

Personalized alignment of large language models seeks to adapt responses to individual user preferences, typically via reinforcement learning. A key challenge is obtaining accurate, user-specific reward signals in open-ended scenarios. Existing personalized reward models face two persistent limitations: (1) oversimplifying diverse, scenario-specific preferences into a small, fixed set of evaluation principles, and (2) struggling with generalization to new users with limited feedback. To this end, we propose **P-GenRM**, the first **P**ersonalized **Gen**erative **R**eward **M**odel with test-time user-based scaling. P-GenRM transforms preference signals into structured evaluation chains that derive adaptive personas and scoring rubrics across various scenarios. It further clusters users into User Prototypes and introduces a dual-granularity scaling mechanism: at the individual level, it adaptively scales and aggregates each user’s scoring scheme; at the prototype level, it incorporates preferences from similar users. This design mitigates noise in inferred preferences and enhances generalization to unseen users through prototype-based transfer. Empirical results show that P-GenRM achieves state-of-the-art results on widely-used personalized reward model benchmarks, with an average improvement of ~2.31\%, and demonstrates strong generalization on an out-of-distribution dataset. Notably, Test-time User-based scaling provides an additional ~3\% boost, demonstrating stronger personalized alignment with test-time scalability.

Diffusion large language models (dLLMs) have recently drawn considerable attention within the research community as a promising alternative to autoregressive generation, offering parallel token prediction and lower inference latency. Yet, their parallel decoding potential remains largely underexplored, as existing open-source models still require nearly token-length decoding steps to ensure performance. To address this, we introduce dParallel, a simple and effective method that unlocks the inherent parallelism of dLLMs for fast sampling. We identify that the key bottleneck to parallel decoding arises from the sequential certainty convergence for masked tokens. Building on this insight, we introduce the core of our approach: certainty-forcing distillation, a novel training strategy that distills the model to follow its original sampling trajectories while enforcing it to achieve high certainty on masked tokens more rapidly and in parallel. Extensive experiments demonstrate that our method can dramatically reduce the number of decoding steps while maintaining performance. When applied to the LLaDA-8B-Instruct model, dParallel reduces decoding steps from 256 to 30 on GSM8K, achieving an 8.5× speedup without performance degradation. On the MBPP benchmark, it cuts decoding steps from 256 to 24, resulting in a 10.5× speedup while maintaining accuracy.

Modern deep neural networks remain challenging to interpret due to the opacity of their latent representations, impeding model understanding, debugging, and debiasing. Concept Embedding Models (CEMs) address this by mapping inputs to human-interpretable concept representations from which tasks can be predicted. Yet, CEMs fail to represent inter-concept relationships and require concept annotations at different granularities during training, limiting their applicability. In this paper, we introduce *Hierarchical Concept Embedding Models* (HiCEMs), a new family of CEMs that explicitly model concept relationships through hierarchical structures. To enable HiCEMs in real-world settings, we propose *Concept Splitting*, a method for automatically discovering finer-grained sub-concepts from a pretrained CEM’s embedding space without requiring additional annotations. This allows HiCEMs to generate fine-grained explanations from limited concept labels, reducing annotation burdens. Our evaluation across multiple datasets, including a user study and experiments on *PseudoKitchens*, a newly proposed concept-based dataset of 3D kitchen renders, demonstrates that (1) Concept Splitting discovers human-interpretable sub-concepts absent during training that can be used to train highly accurate HiCEMs, and (2) HiCEMs enable powerful test-time concept interventions at different granularities, leading to improved task accuracy.

Masked discrete diffusion models have been gaining popularity recently, and classifier-free guidance, just like its continuous counterpart, has been proposed to enable efficacious conditional generation by discrete diffusion. To quantify the precise effect of discrete guidance, this article considers masked discrete diffusion with arbitrary data distribution in low dimension, so that the distribution that guided masked discrete diffusion samples from, as well as the sampling dynamics, can be analytically and exactly quantified and interpreted. When the full data distribution is a mixture over classes and the goal is to sample from a specific class, guidance amplifies class-specific regions while suppresses regions shared with other classes. This effect depends on the guidance strength $w$ and induces distinct covariance structures in the sampled distribution. Notably, we observe quantitatively different behaviors in $1$D and $2$D. We also show that for large $w$, the decay rate of the total variation ($\text{TV}$) along the reverse dynamics is double-exponential in $w$ for both $1$D and $2$D. These findings highlight the role of guidance, not just in shaping the output distribution, but also in controlling the dynamics of the sampling trajectory. Our theoretical analysis is supported by experiments that illustrate the geometric effects of guidance and its impact on convergence.

With the rapid adoption of diffusion models for visual content generation, proving authorship and protecting copyright have become critical. This challenge is particularly important when model owners keep their models private and may be unwilling or unable to handle authorship issues, making third-party verification essential. A natural solution is to embed watermarks for later verification. However, existing methods require access to model weights and rely on computationally heavy procedures, rendering them impractical and non-scalable. To address these challenges, we propose $\text{\emph{NoisePrints}}$, a lightweight watermarking scheme that utilizes the random seed used to initialize the diffusion process as a proof of authorship without modifying the generation process. Our key observation is that the initial noise derived from a seed is highly correlated with the generated visual content. By incorporating a hash function into the noise sampling process, we further ensure that recovering a valid seed from the content is infeasible. We also show that sampling an alternative seed that passes verification is infeasible, and demonstrate the robustness of our method under various manipulations. Finally, we show how to use cryptographic zero-knowledge proofs to prove ownership without revealing the seed. By keeping the seed secret, we increase the difficulty of watermark removal. In our experiments, we validate NoisePrints on multiple state-of-the-art diffusion models for images and videos, demonstrating efficient verification using only the seed and output, without requiring access to model weights.

Flow Matching (FM) has recently emerged as a powerful approach for high-quality visual generation. However, their prohibitively slow inference due to a large number of denoising steps limits their potential use in real-time or interactive applications. Existing acceleration methods, like distillation, truncation, or consistency training, either degrade quality, incur costly retraining, or lack generalization. We propose FlowCast, a training-free speculative generation framework that accelerates inference by exploiting the fact that FM models are trained to preserve constant velocity. FlowCast speculates future velocity by extrapolating current velocity without incurring additional cost, and accepts it if it is within a mean-squared error threshold. This constant-velocity forecasting allows redundant steps in stable regions to be aggressively skipped while retaining precision in complex ones. FlowCast is a plug-and-play framework that integrates seamlessly with any FM model and requires no auxiliary networks. We also present a theoretical analysis and bound the worst-case deviation between speculative and full FM trajectories. Empirical evaluations demonstrate that FlowCast achieves $>2.5\times$ speedup in image generation, video generation, and editing tasks, outperforming existing baselines with no quality loss as compared to standard full generation.

The brain interprets visual information through learned regularities, a computation formalized as performing probabilistic inference under a prior. The visual cortex establishes priors for this inference, some of which are delivered through widely established top-down connections that inform low-level cortices about statistics represented at higher levels in the cortical hierarchy. While evidence supports that adaptation leads to priors reflecting the structure of natural images, it remains unclear if similar priors can be flexibly acquired when learning a specific task. To investigate this, we built a generative model of V1 that we optimized for performing a simple discrimination task and analyzed it along with large scale recordings from mice performing an analogous task. In line with recent successful approaches, we assumed that neuronal activity in V1 can be identified with latent posteriors in the generative model, providing an opportunity to investigate the contributions of task-related priors to neuronal responses. To obtain a flexible test bed for this analysis, we extended the VAE formalism so that a task can be flexibly and data-efficiently acquired by reusing previously learned representations. Task-specific priors learned by this Task-Amortized VAE were used to investigate biases in mice and model when presenting stimuli that violated the trained task statistics. Mismatch between learned task statistics and incoming sensory evidence showed signatures of uncertainty in stimulus category in the posterior of TAVAE, reflecting properties of bimodal response profile in V1 recordings. The task-optimized generative model could account for various characteristics of V1 population activity, including within-day updates to the population responses. Our results confirm that flexible task-specific contextual priors can be learned on-demand by the visual system and can be deployed as early as the entry level of the visual cortex.

Squared tensor networks (TNs) and their extension as computational graphs---squared circuits---have been used as expressive distribution estimators, yet supporting closed-form marginalization. However, the squaring operation introduces additional complexity when computing the partition function or marginalizing variables, which hinders their applicability in ML. To solve this issue, canonical forms of TNs are parameterized via unitary matrices to simplify the computation of marginals. However, these canonical forms do not apply to circuits, as they can represent factorizations that do not directly map to a known TN. Inspired by the ideas of orthogonality in canonical forms and determinism in circuits enabling tractable maximization, we show how to parameterize squared circuits to overcome their marginalization overhead. Our parameterizations unlock efficient marginalization even in factorizations different from TNs, but encoded as circuits, whose structure would otherwise make marginalization computationally hard. Finally, our experiments on distribution estimation show how our proposed conditions in squared circuits come with no expressiveness loss, while enabling more efficient learning.

Diffusion language models (DLMs) have recently emerged as an alternative to autoregressive approaches, offering parallel sequence generation and flexible token orders. However, their inference remains slower than that of autoregressive models, primarily due to the cost of bidirectional attention and the large number of refinement steps required for high-quality outputs. In this work, we highlight and leverage an overlooked property of DLMs, **early answer convergence**: in many cases, the correct answer can be internally identified by half steps before the final decoding step, both under semi-autoregressive and random re-masking schedules. For example, on GSM8K and MMLU, up to 97\% and 99\% of instances, respectively, can be decoded correctly using only half of the refinement steps. Building on this observation, we introduce **Prophet**, a training-free fast decoding paradigm that enables **early commit decoding**. Specifically, Prophet dynamically decides whether to continue refinement or to go ''all-in'' (i.e., decode all remaining tokens in one step), using the confidence gap between the top-2 prediction candidates as the criterion. It integrates seamlessly into existing DLM implementations, incurs negligible overhead, and requires no additional training. Empirical evaluations of LLaDA-8B and Dream-7B across multiple tasks show that Prophet reduces the number of decoding steps by up to 3.4$\times$ while preserving high generation quality. These results recast DLM decoding as a problem of ''when to stop refinement'', and demonstrate that early decode convergence provides a simple yet powerful mechanism for accelerating DLM inference, complementary to existing speedup techniques. Our code is submitted.

Molecular dynamics (MD) simulation has long been the principal computational tool for exploring protein conformational landscapes, but its application is limited by high computational cost. We present ProTDyn, a foundation protein language model that unifies conformational ensemble generation and multi-timescale dynamics modeling within a single framework. Unlike prior approaches that treat these tasks separately, ProTDyn allows flexible i.i.d ensemble sampling and dynamic trajectory simulation. Across diverse protein systems, ProTDyn yields thermodynamically consistent ensembles, faithfully reproduces dynamical properties over multiple timescales, and generalizes to proteins beyond its training data—offering a scalable and efficient alternative to conventional MD simulations.

Autoregressive video diffusion models are capable of extremely long rollouts that are stable and consistent with history, but they are unable to guide the current generation with conditioning from the future. In camera-guided video generation with a predefined camera trajectory, this limitation leads to collisions with the generated scene, after which autoregression quickly collapses. To address this, we propose Generative View Stitching (GVS), which samples the entire sequence in parallel such that the generated scene is faithful to every part of the predefined camera trajectory. Our main contribution is a sampling algorithm that extends prior work on diffusion stitching for robot planning to video generation. While such stitching methods usually require a specially trained model, GVS is compatible with any off-the-shelf video model trained with Diffusion Forcing, a prevalent sequence diffusion framework that we show already provides the affordances necessary for stitching. We then introduce OmniGuidance, a technique that enhances the temporal consistency in stitching by conditioning on both the past and future, and that enables our proposed loop-closing mechanism for delivering long-range coherence. Overall, GVS achieves camera-guided video generation that is stable, collision-free, frame-to-frame consistent, and closes loops for a variety of predefined camera paths, including Oscar Reutersvärd’s Impossible Staircase.

Diffusion models generate data by removing noise gradually, which corresponds to the time-reversal of a noising process. However, access to only the denoising kernels is often insufficient. In many applications, we need the knowledge of the marginal densities along the generation trajectory, which enables tasks such as inference-time control. To address this gap, in this paper, we introduce the Radon-Nikodym Estimator (RNE). Based on the concept of the density ratio between path distributions, it reveals a fundamental connection between marginal densities and transition kernels, providing a flexible plug-and-play framework that unifies (1) diffusion density estimation, (2) inference-time control, and (3) energy-based diffusion training under a single perspective. Experiments demonstrated that RNE delivers strong results in inference-time control applications, such as annealing and model composition, with promising inference-time scaling performance, and achieves simple yet efficient regularisation for training energy-based diffusion models. Additionally, our proposed RNE is modality-agnostic and applicable not only to continuous diffusion models but also to their discrete diffusion counterparts.

This paper introduces *quasi-Monte Carlo latent variable models* (QLVMs): a class of deep generative models that are specialized for finding extremely low-dimensional and interpretable embeddings of high-dimensional datasets. Unlike standard approaches, which rely on a learned encoder and variational lower bounds, QLVMs directly approximate the marginal likelihood by randomized quasi-Monte Carlo integration. While this brute force approach has drawbacks in higher-dimensional spaces, we find that it excels in fitting one, two, and three dimensional deep latent variable models. Empirical results on a range of datasets show that QLVMs consistently outperform conventional variational autoencoders (VAEs) and importance weighted autoencoders (IWAEs) with matched latent dimensionality. The resulting embeddings enable transparent visualization and *post hoc* analyses such as nonparametric density estimation, clustering, and geodesic path computation, which are nontrivial to validate in higher-dimensional spaces. While our approach is compute-intensive and struggles to generate fine-scale details in complex datasets, it offers a compelling solution for applications prioritizing interpretability and latent space analysis.

Classifier-Free Guidance (CFG) is widely used to improve conditional fidelity in diffusion models, but its impact on sampling dynamics remains poorly understood. Prior studies, often restricted to unimodal conditional distributions or simplified cases, provide only a partial picture. We analyze CFG under multimodal conditionals and show that the sampling process unfolds in three successive stages. In the Direction Shift stage, guidance accelerates movement toward the weighted mean, introducing initialization bias and norm growth. In the Mode Separation stage, local dynamics remain largely neutral, but the inherited bias suppresses weaker modes, reducing global diversity. In the Concentration stage, guidance amplifies within-mode contraction, diminishing fine-grained variability. This unified view explains a widely observed phenomenon: stronger guidance improves semantic alignment but inevitably reduces diversity. Experiments support these predictions, showing that early strong guidance erodes global diversity, while late strong guidance suppresses fine-grained variation. Moreover, our theory naturally suggests a time-varying guidance schedule, and empirical results confirm that it consistently improves both quality and diversity.

Building efficient and effective generative models for neural network weights has been a research focus of significant interest that faces challenges posed by the high-dimensional weight spaces of modern neural networks and their symmetries. Several prior generative models are limited to generating partial neural network weights, particularly for larger models, such as ResNet and ViT. Those that do generate complete weights struggle with generation speed or require finetuning of the generated models. In this work, we present \ours, a Flow Matching model that operates directly in weight space to generate diverse and high-accuracy neural network weights for a variety of architectures, neural network sizes, and data modalities. The neural networks generated by \ours do not require fine-tuning to perform well and can scale to large networks. We apply Git Re-Basin and TransFusion for neural network canonicalization in the context of generative weight models to account for the impact of neural network permutation symmetries and to improve generation efficiency for larger model sizes. The generated networks excel at transfer learning, and ensembles of hundreds of neural networks can be generated in minutes, far exceeding the efficiency of diffusion-based methods. DeepWeightFlow models pave the way for more efficient and scalable generation of diverse sets of neural networks.

We present Kaleido, a family of generative models designed for photorealistic, unified object- and scene-level neural rendering. Kaleido is driven by the principle of treating 3D as a specialised sub-domain of video, which we formulate purely as a sequence-to-sequence image synthesis task. Through a systemic study of scaling sequence-to-sequence generative neural rendering, we introduce key architectural innovations that enable our model to: i) perform generative view synthesis without explicit 3D representations; ii) generate any number of 6-DoF target views conditioned on any number of reference views via a masked autoregressive framework; and iii) seamlessly unify 3D and video modelling within a single decoder-only rectified flow transformer. Within this unified framework, Kaleido leverages large-scale video data for pre-training, which significantly improves spatial consistency and reduces reliance on scarce, camera-labelled 3D datasets --- all without any architectural modifications. Kaleido sets a new state-of-the-art on a range of view synthesis benchmarks. Its zero-shot performance substantially outperforms other generative methods in few-view settings, and, for the first time, matches the quality of per-scene optimisation methods in many-view settings. For supplementary materials, including Kaleido's generated renderings and videos, please refer to our website: https://shikun.io/projects/kaleido.