ICML 2026 Papers

In this paper, we generate conceptual engineering designs of electric vertical take-off and landing (eVTOL) aircraft. We follow the paradigm of simulation-based inference (SBI), whereby we look to learn a posterior distribution over the full eVTOL design space. To learn this distribution, we sample over discrete aircraft configurations (topologies) and their corresponding set of continuous parameters. Therefore, we introduce a hierarchical probabilistic model consisting of two diffusion models. The first model leverages recent work on Riemannian Diffusion Language Modeling (RDLM) and Unified World Models (UWMs) to enable us to sample topologies from a discrete and continuous space. For the second model we introduce a masked diffusion approach to sample the corresponding parameters conditioned on the topology. Our approach rediscovers known trends and governing physical laws in aircraft design, while significantly accelerating design generation.

Diffusion large language models (dLLMs) are promising alternatives to autoregressive large language models (AR-LLMs), as they potentially allow higher inference throughput. Reinforcement learning (RL) is crucial to enabling dLLMs to achieve performance comparable to that of AR-LLMs on important tasks, such as reasoning. However, RL algorithms well-suited to dLLMs' unique characteristics have yet to be developed. This paper proposes \textbf{Distribution Matching Policy Optimization (DMPO)}, a principled and theoretically grounded RL fine-tuning method specifically designed to enhance the reasoning capabilities of dLLMs by matching the dLLM policy distribution to the optimal, reward-tilted one through cross-entropy optimization. We identify a key implementation challenge with small training batch sizes and propose several effective solutions based on a novel weight baseline subtraction technique. DMPO exhibits superior performance on multiple reasoning benchmarks without supervised fine-tuning, achieving up to a $39.63$ percentage-point improvement in accuracy over prior non-DMPO RL baselines and $67.97$ percentage points over the base model, underscoring the effectiveness of the distribution-matching framework. Our code is available at https://github.com/yuchen-zhu-zyc/DMPO.

Reinforcement learning (RL) with combinatorial action spaces remains challenging because feasible action sets are exponentially large and governed by complex feasibility constraints, making direct policy parameterization impractical. Existing approaches embed task-specific value functions into constrained optimization programs or learn deterministic structured policies, sacrificing generality and policy expressiveness. We propose a solver-induced \emph{latent spherical flow policy} that brings the expressiveness of modern generative policies to combinatorial RL while guaranteeing feasibility by design. Our method, LSFlow, learns a \emph{stochastic} policy in a compact continuous latent space via spherical flow matching, and delegates feasibility to a combinatorial optimization solver that maps each latent sample to a valid structured action. To improve efficiency, we train the value network directly in the latent space, avoiding repeated solver calls during policy optimization. To address the piecewise-constant and discontinuous value landscape induced by solver-based action selection, we introduce a smoothed Bellman operator that yields stable, well-defined learning targets. Empirically, our approach outperforms state-of-the-art baselines by an average of 20.6\% across a range of challenging combinatorial RL tasks.

Many scientific problems require inferring unobserved mechanistic latent states from indirect observations. While classical approaches, including expectation-maximization, do not scale to combinatorially large spaces, deep learning approaches such as variational autoencoders typically form artificial latent states rather than reconstructing the mechanistic ground-truth states. Here, we introduce GReinSS, a policy learning framework that uses dynamically rescaled rewards to learn latent state distributions that maximize the observed data likelihood. We show that GReinSS accurately reconstructs simulated latent sets and latent graphs, outperforming alternative policy learning and generative modeling baselines. Additionally, GReinSS reconstructs isoforms from real short-read RNA sequencing data that better match orthogonal long-read sequencing detected isoforms than the standard RSEM algorithm. Overall, GReinSS is a principled and practically effective approach for generative modeling and inference of combinatorial latent states from indirect observations.

While continuous diffusion has shown remarkable success in continuous domains such as image generation, its direct application to discrete data has underperformed pure discrete formulations. To understand this gap, we introduce *token identifiability*, an analytical framework characterizing how Gaussian noise corrupts discrete data through two mechanisms: *discrete identity corruption* and *continuous rank degradation*. We reveal that these mechanisms scale differently with vocabulary size, creating a *temporal dissonance* that forces a tradeoff between learning continuous geometry and discrete structure. To address this, we propose **CANDI** (**C**ontinuous **AN**d **DI**screte diffusion), a hybrid framework that decouples discrete and continuous corruption, enabling simultaneous learning of both. This unlocks the benefits of continuous diffusion for discrete spaces: on controlled generation, CANDI enables classifier-based guidance with off-the-shelf classifiers through simple gradient addition; on text generation, CANDI outperforms masked diffusion at low NFE, demonstrating the value of learning continuous gradients for discrete spaces.

Test-time scaling strategies have effectively leveraged inference-time compute to enhance the reasoning abilities of Autoregressive Large Language Models. In this work, we demonstrate that Masked Diffusion Language Models (MDLMs) are inherently amenable to advanced search strategies, owing to their iterative and non-autoregressive generation process. To leverage this, we propose **UnMaskFork** (**UMF**), a framework that formulates the unmasking trajectory as a search tree and employs Monte Carlo Tree Search to optimize the generation path. In contrast to standard scaling methods relying on stochastic sampling, UMF explores the search space through deterministic partial unmasking actions performed by multiple MDLMs. Our empirical evaluation demonstrates that UMF consistently outperforms existing test-time scaling baselines on complex coding benchmarks, while also exhibiting strong scalability on mathematical reasoning tasks.

Although diffusion models have revolutionized continuous domains like image synthesis through high quality generations and controllable guidance mechanisms, bringing this controllability to the discrete, sequential nature of text remains an open challenge. Meanwhile, current sampling strategies and guidance methods adjust token likelihoods without capturing the broader semantic landscape, leading to a suboptimal balance between fidelity and diversity. In this work, we introduce a novel training-free Semantic-Aware Kernel Entropy (SAKE) guidance method. Our method computes the order-2 Rényi entropy over a kernel Gram matrix that captures both cross-token semantic interactions and relative token positions. By linearizing this objective in the embedding space, we derive a tractable guidance signal that dynamically adjusts the sampling distribution—flattening it to encourage exploration during redundancy and sharpening it for fidelity when diverse. Empirical experiments demonstrate that our approach achieves a superior Pareto frontier between fidelity and diversity, and improves multi-sample performance on reasoning-intensive tasks, such as code and mathematics generation, compared to temperature scaling and discrete guidance baselines.