Many problems in disordered materials require sampling beyond fixed composition and volume, where coupled changes in atomic identities and structure create a prohibitively expensive discrete-continuous sampling problem. Here we introduce JANUS, a multimodal neural sampler that couples continuous and masked discrete diffusion through an equivariant graph neural network trained directly from energy evaluations, without pre-generated equilibrium data. In benchmark Ising and isobaric ΔμNPT alloy systems, JANUS reproduces reference Monte Carlo equilibrium observables and recovers free energies and phase behavior with more than three orders of magnitude fewer energy evaluations. In multicomponent alloys, JANUS enables conditional steering toward prescribed chemical short-range order and enhanced bulk modulus and, when coupled to a large language model evolutionary agent, performs efficient inverse design for balanced optical and mechanical properties. In semiconductors like silicon and diamond, JANUS explores vacancies and dopants spanning 15 elements in grand-canonical μVT ensembles, recovers established defects including the silicon E centre, and identifies new candidate defect pairs and triplets for quantum engineering, including S-Ti in silicon and B-O-O in diamond, with deep in-gap states validated by hybrid-functional density functional theory. By unifying discrete site identities with continuous structural and volumetric relaxation, JANUS provides a foundation for thermodynamic sampling, characterization and inverse design of chemically disordered materials.

Sampling from unnormalized densities using diffusion models has emerged as a powerful paradigm. However, while recent approaches that use least-squares `matching' objectives have improved scalability, they often necessitate significant trade-offs, such as restricting prior distributions or relying on unstable optimization schemes. By generalizing these methods as special forms of fixed-point iterations rooted in Nelson's relation, we develop a new method that addresses these limitations. Our approach enables learning a stochastic transport map between arbitrary prior and target distributions with a single, scalable, and stable objective. Furthermore, we introduce a damped variant of this iteration that incorporates a regularization term to mitigate mode collapse. Empirically, we demonstrate that our method enables sampling at unprecedented scales while preserving mode diversity, achieving state-of-the-art results on complex synthetic densities and high-dimensional molecular benchmarks.

Efficient sampling from high-dimensional and multimodal unnormalized probability distributions is a central challenge in many areas of science and machine learning. We focus on Boltzmann generators (BGs) that aim to sample the Boltzmann distribution of physical systems, such as molecules, at a given temperature. Classical variational approaches that minimize the reverse Kullback–Leibler divergence are prone to mode collapse, while annealing-based methods, commonly using geometric schedules, can suffer from mass teleportation and rely heavily on schedule tuning. We introduce *Constrained Mass Transport* (CMT), a variational framework that generates intermediate distributions under constraints on both the KL divergence and the entropy decay between successive steps. These constraints enhance distributional overlap, mitigate mass teleportation, and counteract premature convergence. Across standard BG benchmarks and the here introduced *ELIL tetrapeptide*, the largest system studied to date without access to samples from molecular dynamics, CMT consistently surpasses state-of-the-art variational methods, achieving more than 2.5× higher effective sample size while avoiding mode collapse.

Diffusion policies have recently emerged as a powerful paradigm for representing complex action distributions in reinforcement learning (RL). However, their application to online RL remains limited by the challenge of scalable training in the absence of ground-truth data, where standard optimization techniques such as score matching are not directly applicable. In this work, we introduce a highly efficient algorithm for optimizing diffusion policies by leveraging recent advances in stochastic optimal control. Our approach is based on adjoint matching, which enables simulation-free training and circumvents the need for explicit likelihood estimation or costly backpropagation through the diffusion process. Furthermore, we propose several extensions that improve the robustness and stability of the method in practical settings. Empirical results demonstrate that our approach achieves competitive performance while significantly reducing computational overhead, making diffusion policies more viable for online RL scenarios.

Reinforcement learning with massively parallel simulations has become an emerging trend; however, most existing approaches still rely on simple Gaussian policy parameterizations. Diffusion models provide a more expressive policy class and have shown strong performance on challenging control problems, yet most diffusion-based RL methods are designed for offline or off-policy training. In this work, we ask whether diffusion policies can be trained effectively in the massively parallel, on-policy regime. To this end, we introduce Trust-region Diffusion Policies (TruDi), which enables diffusion policies for on-policy RL with massively parallel simulations. This setting is particularly challenging because the data distribution changes quickly across updates, making stable training with complex policies difficult. TruDi addresses this by integrating a trust-region optimization rule to enforce a KL-divergence constraint over the entire diffusion trajectory, rather than only at the final denoising step. Empirically, we evaluate TruDi on a diverse set of 4 massively parallel RL benchmarks comprising a total of 73 tasks. Across these tasks, TruDi consistently outperforms or is on-par with strong baselines on standard tasks and achieves clear gains on more challenging humanoid control tasks, establishing a strong new baseline for massively parallel on-policy RL.

Amorphous materials exhibit exceptional mechanical and functional properties, yet their rugged energy landscapes are notoriously difficult to sample. Below the glass-transition temperature, conventional molecular dynamics and Monte Carlo become inefficient because equilibration relies on rare barrier-crossing events, while data-driven generative models are constrained by scarce and biased reference ensembles. Here, we introduce ATLAS, an efficient sampler that learns a diffusion process to generate Boltzmann-distributed amorphous structures directly from a target energy function. Parameterized by an equivariant graph neural network, ATLAS generalizes across system size, temperature, and composition. By exploiting the time reversal of the diffusion process, it enables efficient estimation of thermodynamic quantities and steering toward target observables. In two-dimensional Kob-Andersen systems, ATLAS reproduces parallel tempering Markov chain Monte Carlo structural distributions, free energies and entropies, achieving below 0.2

An effective approach for sampling from unnormalized densities is based on the idea of gradually transporting samples from an easy prior to the complicated target distribution. Two popular methods are (1) Sequential Monte Carlo (SMC), where the transport is performed through successive annealed densities via prescribed Markov chains and resampling steps, and (2) recently developed diffusion-basedsampling methods, where a learned dynamical transport is used. Despite the common goal, both approaches have different, often complementary, advantages and drawbacks. The resampling steps in SMC allow focusing on promising regions of the space, often leading to robust performance. While the algorithm enjoys asymptotic guarantees, the lack of flexible, learnable transitions can lead to slow convergence. On the other hand, diffusion-based samplers are learned and can potentially better adapt themselves to the target at hand, yet often suffer from training instabilities. In this work, we present a principled framework for combining SMC with diffusion-based samplers by viewing both methods in continuous time and considering measures on path space. This culminates in the new Sequential Controlled Langevin Diffusion (SCLD) sampling method, which is able to utilize the benefits of both methods and reaches improved performance on multiple benchmark problems, in many cases using only 10% of the training budget of previous diffusion-based samplers.

Maximum entropy reinforcement learning (MaxEnt-RL) has become the standard approach to RL due to its beneficial exploration properties. Traditionally, policies are parameterized using Gaussian distributions, which significantly limits their representational capacity. Diffusion-based policies offer a more expressive alternative, yet integrating them into MaxEnt-RL poses challenges-primarily due to the intractability of computing their marginal entropy. To overcome this, we propose Diffusion-Based Maximum Entropy RL (DIME). DIME leverages recent advances in approximate inference with diffusion models to derive a lower bound on the maximum entropy objective. Additionally, we propose a policy iteration scheme that provably converges to the optimal diffusion policy. Our method enables the use of expressive diffusion-based policies while retaining the principled exploration benefits of MaxEnt-RL, significantly outperforming other diffusion-based methods on challenging high-dimensional control benchmarks. It is also competitive with state-of-the-art non-diffusion based RL methods while requiring fewer algorithmic design choices and smaller update-to-data ratios, reducing computational complexity.

Learning for manipulation requires using policies that have access to rich sensory information such as point clouds or RGB images. Point clouds efficiently capture geometric structures, making them essential for manipulation tasks in imitation learning. In contrast, RGB images provide rich texture and semantic information that can be crucial for certain tasks. Existing approaches for fusing both modalities assign 2D image features to point clouds. However, such approaches often lose global contextual information from the original images. In this work, we propose a novel imitation learning method that effectively combines the strengths of both point cloud and RGB modalities. Our method conditions the point-cloud encoder on global and local image tokens using adaptive layer norm conditioning, leveraging the beneficial properties of both modalities. Through extensive experiments on the challenging RoboCasa benchmark, we demonstrate the limitations of relying on either modality alone and show that our method achieves state-of-the-art performance across all tasks.

We provide a general framework for learning diffusion bridges that transport prior to target distributions. It includes existing diffusion models for generative modeling, but also underdamped versions with degenerate diffusion matrices, where the noise only acts in certain dimensions. Extending previous findings, our framework allows to rigorously show that score-matching in the underdamped case is indeed equivalent to maximizing a lower bound on the likelihood. Motivated by superior convergence properties and compatibility with sophisticated numerical integration schemes of underdamped stochastic processes, we propose *underdamped diffusion bridges*, where a general density evolution is learned rather than prescribed by a fixed noising process. We apply our method to the challenging task of sampling from unnormalized densities without access to samples from the target distribution. Across a diverse range of sampling problems, our approach demonstrates state-of-the-art performance, notably outperforming alternative methods, while requiring significantly fewer discretization steps and almost no hyperparameter tuning.

Accurately simulating physics is crucial across scientific domains, with applications spanning from robotics to materials science. While traditional mesh-based simulations are precise, they are often computationally expensive and require knowledge of physical parameters, such as material properties. In contrast, data-driven approaches like Graph Network Simulators (GNSs) offer faster inference but suffer from two key limitations: Firstly, they must be retrained from scratch for even minor variations in physical parameters, and secondly they require labor-intensive data collection for each new parameter setting. This is inefficient, as simulations with varying parameters often share a common underlying latent structure. In this work, we address these challenges by learning this shared structure through meta-learning, enabling fast adaptation to new physical parameters without retraining. To this end, we propose a novel architecture that generates a latent representation by encoding graph trajectories using conditional neural processes (CNPs). To mitigate error accumulation over time, we combine CNPs with a novel neural operator architecture. We validate our approach, Meta Neural Graph Operator (MaNGO), on several dynamics prediction tasks with varying material properties, demonstrating superior performance over existing GNS methods. Notably, MaNGO achieves accuracy on unseen material properties close to that of an oracle model.

Dexterous robotic hands are essential for performing complex manipulation tasks, yet remain difficult to train due to the challenges of demonstration collection and high-dimensional control. While reinforcement learning (RL) can alleviate the data bottleneck by generating experience in simulation, it typically relies on carefully designed, task-specific reward functions, which hinder scalability and generalization. Thus, contemporary works in dexterous manipulation have often bootstrapped from reference trajectories. These trajectories specify target hand poses that guide the exploration of RL policies and object poses that enable dense, task-agnostic rewards. However, sourcing suitable trajectories - particularly for dexterous hands - remains a significant challenge. Yet, the precise details in explicit reference trajectories are often unnecessary, as RL ultimately refines the motion. Our key insight is that modern vision-language models (VLMs) already encode the commonsense spatial and semantic knowledge needed to specify tasks and guide exploration effectively. Given a task description (e.g., "open the cabinet") and a visual scene, our method uses an off-the-shelf VLM to first identify task-relevant keypoints (e.g., handles, buttons) and then synthesize 3D trajectories for hand motion and object motion. Subsequently, we train a low-level residual RL policy in simulation to track these coarse trajectories or "scaffolds" with high fidelity. Across a number of simulated tasks involving articulated objects and semantic understanding, we demonstrate that our method is able to learn robust dexterous manipulation policies. Moreover, we showcase that our method transfers to real-world robotic hands without any human demonstrations or handcrafted rewards.

Solving stochastic optimal control problems with quadratic control costs can be viewed as approximating a target path space measure, e.g. via gradient-based optimization. In practice, however, this optimization is challenging in particular if the target measure differs substantially from the prior. In this work, we therefore approach the problem by iteratively solving constrained problems incorporating trust regions that aim for approaching the target measure gradually in a systematic way. It turns out that this trust region based strategy can be understood as a geometric annealing from the prior to the target measure, where, however, the incorporated trust regions lead to a principled and educated way of choosing the time steps in the annealing path. We demonstrate in multiple optimal control applications that our novel method can improve performance significantly, including tasks in diffusion-based sampling and fine-tuning of diffusion models.

Designing modern imitation learning (IL) policies requires making numerous decisions, including the selection of feature encoding, architecture, policy representation, and more. As the field rapidly advances, the range of available options continues to grow, creating a vast and largely unexplored design space for IL policies. In this work, we present X-IL, an accessible open-source framework designed to systematically explore this design space. The framework's modular design enables seamless swapping of policy components, such as backbones (e.g., Transformer, Mamba, xLSTM) and policy optimization techniques (e.g., Score-matching, Flow-matching). This flexibility facilitates comprehensive experimentation and has led to the discovery of novel policy configurations that outperform existing methods on recent robot learning benchmarks. Our experiments demonstrate not only significant performance gains but also provide valuable insights into the strengths and weaknesses of various design choices. This study serves as both a practical reference for practitioners and a foundation for guiding future research in imitation learning.

Diffusion models optimized via variational inference (VI) have emerged as a promising tool for generating samples from unnormalized target densities. These models create samples by simulating a stochastic differential equation, starting from a simple, tractable prior, typically a Gaussian distribution. However, when the support of this prior differs greatly from that of the target distribution, diffusion models often struggle to explore effectively or suffer from large discretization errors. Moreover, learning the prior distribution can lead to mode-collapse, exacerbated by the mode-seeking nature of reverse Kullback-Leibler divergence commonly used in VI. To address these challenges, we propose end-to-end learnable Gaussian mixture priors (GMPs). GMPs offer improved control over exploration, adaptability to target support, and increased expressiveness to counteract mode collapse. We further leverage the structure of mixture models by proposing a strategy to iteratively refine the model by adding mixture components during training. Our experimental results demonstrate significant performance improvements across a diverse range of real-world and synthetic benchmark problems when using GMPs without requiring additional target evaluations.

Imitation learning with human data has demonstrated remarkable success in teaching robots in a wide range of skills. However, the inherent diversity in human behavior leads to the emergence of multi-modal data distributions, thereby presenting a formidable challenge for existing imitation learning algorithms. Quantifying a model's capacity to capture and replicate this diversity effectively is still an open problem. In this work, we introduce simulation benchmark environments and the corresponding *Datasets with Diverse human Demonstrations for Imitation Learning (D3IL)*, designed explicitly to evaluate a model's ability to learn multi-modal behavior. Our environments are designed to involve multiple sub-tasks that need to be solved, consider manipulation of multiple objects which increases the diversity of the behavior and can only be solved by policies that rely on closed loop sensory feedback. Other available datasets are missing at least one of these challenging properties. To address the challenge of diversity quantification, we introduce tractable metrics that provide valuable insights into a model's ability to acquire and reproduce diverse behaviors. These metrics offer a practical means to assess the robustness and versatility of imitation learning algorithms. Furthermore, we conduct a thorough evaluation of state-of-the-art methods on the proposed task suite. This evaluation serves as a benchmark for assessing their capability to learn diverse behaviors. Our findings shed light on the effectiveness of these methods in tackling the intricate problem of capturing and generalizing multi-modal human behaviors, offering a valuable reference for the design of future imitation learning algorithms.

Monte Carlo methods, Variational Inference, and their combinations play a pivotal role in sampling from intractable probability distributions. However, current studies lack a unified evaluation framework, relying on disparate performance measures and limited method comparisons across diverse tasks, complicating the assessment of progress and hindering the decision-making of practitioners. In response to these challenges, our work introduces a benchmark that evaluates sampling methods using a standardized task suite and a broad range of performance criteria. Moreover, we study existing metrics for quantifying mode collapse and introduce novel metrics for this purpose. Our findings provide insights into strengths and weaknesses of existing sampling methods, serving as a valuable reference for future developments. The code is publicly available here.

This work presents Mamba Imitation Learning (MaIL), a novel imitation learning (IL) architecture that provides an alternative to state-of-the-art (SoTA) Transformer-based policies. MaIL leverages Mamba, a state-space model designed to selectively focus on key features of the data. While Transformers are highly effective in data-rich environments due to their dense attention mechanisms, they can struggle with smaller datasets, often leading to overfitting or sub-optimal representation learning. In contrast, Mamba's architecture enhances representation learning efficiency by focusing on key features and reducing model complexity. This approach mitigates overfitting and enhances generalization, even when working with limited data. Extensive evaluations on the LIBERO benchmark demonstrate that MaIL consistently outperforms Transformers on all LIBERO tasks with limited data and matches their performance when the full dataset is available. Additionally, MaIL's effectiveness is validated through its superior performance in three real robot experiments. Our code is available at https://github.com/ALRhub/MaIL.

This work introduces Variational Diffusion Distillation (VDD), a novel method that distills denoising diffusion policies into Mixtures of Experts (MoE) through variational inference. Diffusion Models are the current state-of-the-art in generative modeling due to their exceptional ability to accurately learn and represent complex, multi-modal distributions. This ability allows Diffusion Models to replicate the inherent diversity in human behavior, making them the preferred models in behavior learning such as Learning from Human Demonstrations (LfD). However, diffusion models come with some drawbacks, including the intractability of likelihoods and long inference times due to their iterative sampling process. The inference times, in particular, pose a significant challenge to real-time applications such as robot control. In contrast, MoEs effectively address the aforementioned issues while retaining the ability to represent complex distributions but are notoriously difficult to train. VDD is the first method that distills pre-trained diffusion models into MoE models, and hence, combines the expressiveness of Diffusion Models with the benefits of Mixture Models. Specifically, VDD leverages a decompositional upper bound of the variational objective that allows the training of each expert separately, resulting in a robust optimization scheme for MoEs. VDD demonstrates across nine complex behavior learning tasks, that it is able to: i) accurately distill complex distributions learned by the diffusion model, ii) outperform existing state-of-the-art distillation methods, and iii) surpass conventional methods for training MoE. The code and videos are available at https://intuitive-robots.github.io/vdd-website.

This work introduces Mamba Imitation Learning (MaIL), a novel imitation learning (IL) architecture that offers a computationally efficient alternative to state-of-the-art (SoTA) Transformer policies. Transformer-based policies have achieved remarkable results due to their ability in handling human-recorded data with inherently non-Markovian behavior. However, their high performance comes with the drawback of large models that complicate effective training. While state space models (SSMs) have been known for their efficiency, they were not able to match the performance of Transformers. Mamba significantly improves the performance of SSMs and rivals against Transformers, positioning it as an appealing alternative for IL policies. MaIL leverages Mamba as a backbone and introduces a formalism that allows using Mamba in the encoder-decoder structure. This formalism makes it a versatile architecture that can be used as a standalone policy or as part of a more advanced architecture, such as a diffuser in the diffusion process. Extensive evaluations on the LIBERO IL benchmark and three real robot experiments show that MaIL: i) outperforms Transformers in all LIBERO tasks, ii) achieves good performance even with small datasets, iii) is able to effectively process multi-modal sensory inputs, iv) is more robust to input noise compared to Transformers.