NeurIPS 2025 Papers

Computational methods for learning to sample from the Boltzmann distribution—where the target distribution is known only up to an unnormalized energy function—have advanced significantly recently. Due to the lack of explicit target samples, however, prior diffusion-based methods, known as _diffusion samplers_, often require importance-weighted estimation or complicated learning processes. Both trade off scalability with extensive evaluations of the energy and model, thereby limiting their practical usage. In this work, we propose **Adjoint Schrödinger Bridge Sampler (ASBS)**, a new diffusion sampler that employs simple and scalable matching-based objectives yet without the need to estimate target samples during training. ASBS is grounded on a mathematical model—the Schrödinger Bridge—which enhances sampling efficiency via kinetic-optimal transportation. Through a new lens of stochastic optimal control theory, we demonstrate how SB-based diffusion samplers can be learned at scale via Adjoint Matching and prove convergence to the global solution. Notably, ASBS generalizes the recent Adjoint Sampling (Havens et al., 2025) to arbitrary source distributions by relaxing the so-called memoryless condition that largely restricts the design space. Through extensive experiments, we demonstrate the effectiveness of ASBS on sampling from classical energy functions, amortized conformer generation, and molecular Boltzmann distributions. Codes are available at https://github.com/facebookresearch/adjoint_samplers

The advancement of AI systems for mental health support is hindered by limited access to therapeutic conversation data, particularly for trauma treatment. We present Thousand Voices of Trauma, a synthetic benchmark dataset of 3,000 therapy conversations based on Prolonged Exposure therapy protocols for Post-traumatic Stress Disorder (PTSD). The dataset comprises 500 unique cases, each explored through six conversational perspectives that mirror the progression of therapy from initial anxiety to peak distress to emotional processing. We incorporated diverse demographic profiles (ages 18-80, M=49.3, 49.4\% male, 44.4\% female, 6.2\% non-binary), 20 trauma types, and 10 trauma-related behaviors using deterministic and probabilistic generation methods. Analysis reveals realistic distributions of trauma types (witnessing violence 10.6\%, bullying 10.2\%) and symptoms (nightmares 23.4\%, substance abuse 20.8\%). Clinical experts validated the dataset's therapeutic fidelity, highlighting its emotional depth while suggesting refinements for greater authenticity. We also developed an emotional trajectory benchmark with standardized metrics for evaluating model responses. This privacy-preserving dataset addresses critical gaps in trauma-focused mental health data, offering a valuable resource for advancing both patient-facing applications and clinician training tools.

We propose a novel diffusion-based framework for automatic colorization of Anime-style facial sketches, which preserves the structural fidelity of the input sketch while effectively transferring stylistic attributes from a reference image. Our approach builds upon recent continuous-time diffusion models, but departs from traditional methods that rely on predefined noise schedules, which often fail to maintain perceptual consistency across the generative trajectory. To address this, we introduce SSIMBaD (Sigma Scaling with SSIM-Guided Balanced Diffusion), a sigma-space transformation that ensures linear alignment of perceptual degradation, as measured by structural similarity. This perceptual scaling enforces uniform visual difficulty across timesteps, enabling more balanced and faithful reconstructions. On a large-scale Anime face dataset, SSIMBaD attains state-of-the-art structural fidelity and strong perceptual quality, with robust generalization to diverse styles and structural variations.

Fusing multimodal brain imaging has been a hot topic since different modalities of brain imaging can provide complementary information. However, due to the size of simultaneous recorded fMRI-EEG dataset being limited and the substantial discrepancy between hemodynamic responses of fMRI and neural oscillations of EEG, the joint modeling of fMRI and EEG images is a rarely explored area and has not yielded satisfactory results. Existing studies have also indicated that the relationships between region of interest (ROI) are not one-to-one when synchronizing fMRI and EEG. Current graph-based multimodal modeling methods overlook those information. Based on this, we propose a hypergraph based fMRI-EEG modeling framework for asynchronous fMRI-EEG data named FE-NET. To the best of our knowledge, this is the first attempt to jointly model asynchronous EEG and fMRI data as Neural ODEs based hypergraph. Extensive experiments have demonstrated that the proposed FE-NET outperforms many state-of-the-art brain imaging modeling methods. Meanwhile, compared to simultaneously recorded fMRI-EEG data, asynchronously acquired fMRI-EEG data is less costly, which demonstrates the practical applicability of our method.

Transformer-based algorithms, such as LoRAT, have significantly enhanced object-tracking performance. However, these approaches rely on a standard attention mechanism, which incurs quadratic token complexity, making real-time inference computationally expensive. In this paper, we introduce LoRATv2, a novel tracking framework that addresses these limitations with three main contributions. First, LoRATv2 integrates frame-wise causal attention, which ensures full self-attention within each frame while enabling causal dependencies across frames, significantly reducing computational overhead. Moreover, key-value (KV) caching is employed to efficiently reuse past embeddings for further speedup. Second, building on LoRAT's parameter-efficient fine-tuning, we propose Stream-Specific LoRA Adapters (SSLA). As frame-wise causal attention introduces asymmetry in how streams access temporal information, SSLA assigns dedicated LoRA modules to the template and each search stream, with the main ViT backbone remaining frozen. This allows specialized adaptation for each stream's role in temporal tracking. Third, we introduce a two-phase progressive training strategy, which first trains a single-search-frame tracker and then gradually extends it to multi-search-frame inputs by introducing additional LoRA modules. This curriculum-based learning paradigm improves long-term tracking while maintaining training efficiency. In extensive experiments on multiple benchmarks, LoRATv2 achieves state-of-the-art performance, substantially improved efficiency, and a superior performance-to-FLOPs ratio over state-of-the-art trackers. The code is available at https://github.com/LitingLin/LoRATv2.

While large transformer models excel in predictive performance, their lack of interpretability restricts their usefulness in high-stakes domains. To remedy this, we propose the Generalized Induction-Head Model (GIM), an interpretable model for next-token prediction inspired by the observation of “induction heads” in LLMs. GIM is a retrieval-based module that identifies similar sequences in the input context by combining exact n-gram matching and fuzzy matching based on a neural similarity metric. We evaluate GIM in two settings: language modeling and fMRI response prediction. In language modeling, GIM improves next-token prediction by up to 25%p over interpretable baselines, significantly narrowing the gap with black-box LLMs. In an fMRI setting, GIM improves neural response prediction by 20% and offers insights into the language selectivity of the brain. GIM represents a significant step toward uniting interpretability and performance across domains. The code is available at https://github.com/ejkim47/generalized-induction-head.

Existing molecular machine learning force fields (MLFFs) generally focus on the learning of atoms, molecules, and simple quantum chemical properties (such as energy and force), but ignore the importance of electron density (ED) $\rho(r)$ in accurately understanding molecular force fields (MFFs). ED describes the probability of finding electrons at specific locations around atoms or molecules, which uniquely determines all ground state properties (such as energy, molecular structure, etc.) of interactive multi-particle systems according to the Hohenberg-Kohn theorem. However, the calculation of ED relies on the time-consuming first-principles density functional theory (DFT), which leads to the lack of large-scale ED data and limits its application in MLFFs. In this paper, we introduce EDBench, a large-scale, high-quality dataset of ED designed to advance learning-based research at the electronic scale. Built upon the PCQM4Mv2, EDBench provides accurate ED data, covering 3.3 million molecules. To comprehensively evaluate the ability of models to understand and utilize electronic information, we design a suite of ED-centric benchmark tasks spanning prediction, retrieval, and generation. Our evaluation of several state-of-the-art methods demonstrates that learning from EDBench is not only feasible but also achieves high accuracy. Moreover, we show that learning-based methods can efficiently calculate ED with comparable precision while significantly reducing the computational cost relative to traditional DFT calculations. All data and benchmarks from EDBench will be freely available, laying a robust foundation for ED-driven drug discovery and materials science.

Generative modeling of time series is a central challenge in time series analysis, particularly under data-scarce conditions. Despite recent advances in generative modeling, a comprehensive understanding of how state-of-the-art generative models perform under limited supervision remains lacking. In this work, we conduct the first large-scale study evaluating leading generative models in data-scarce settings, revealing a substantial performance gap between full-data and data-scarce regimes. To close this gap, we propose a unified diffusion-based generative framework that can synthesize high-fidelity time series across diverse domains using just a few examples. Our model is pretrained on a large, heterogeneous collection of time series datasets, enabling it to learn generalizable temporal representations. It further incorporates architectural innovations such as dynamic convolutional layers for flexible channel adaptation and dataset token conditioning for domain-aware generation. Without requiring abundant supervision, our unified model achieves state-of-the-art performance in few-shot settings—outperforming domain-specific baselines across a wide range of subset sizes. Remarkably, it also surpasses all baselines even when tested on full datasets benchmarks, highlighting the strength of pretraining and cross-domain generalization. We hope this work encourages the community to revisit few-shot generative modeling as a key problem in time series research and pursue unified solutions that scale efficiently across domains. Code is available at https://github.com/azencot-group/ImagenFew.

Molecular dynamics (MD) provides insights into atomic-scale processes by integrating over time the equations that describe the motion of atoms under the action of interatomic forces. Machine learning models have substantially accelerated MD by providing inexpensive predictions of the forces, but they remain constrained to minuscule time integration steps, which are required by the fast time scale of atomic motion. In this work, we propose FlashMD, a method to predict the evolution of positions and momenta over strides that are between one and two orders of magnitude longer than typical MD time steps. We incorporate considerations on the mathematical and physical properties of Hamiltonian dynamics in the architecture, generalize the approach to allow the simulation of any thermodynamic ensemble, and carefully assess the possible failure modes of a direct MD approach. We validate FlashMD’s accuracy in reproducing equilibrium and time‐dependent properties, using both system‐specific and general-purpose models, extending the ability of MD simulation to reach the long time scales needed to model microscopic processes of high scientific and technological relevance.

The molecular large language models have garnered widespread attention due to their promising potential on molecular applications. However, current molecular large language models face significant limitations in understanding molecules due to inadequate textual descriptions and suboptimal molecular representation strategies during pretraining. To address these challenges, we introduce KnowMol-100K, a large-scale dataset with 100K fine-grained molecular annotations across multiple levels, bridging the gap between molecules and textual descriptions. Additionally, we propose chemically-informative molecular representation, effectively addressing limitations in existing molecular representation strategies. Building upon these innovations, we develop KnowMol, a state-of-the-art multi-modal molecular large language model. Extensive experiments demonstrate that KnowMol achieves superior performance across molecular understanding and generation tasks.

We study Diffusion Schrödinger Bridge (DSB) models in the context of dynamical astrophysical systems, specifically tackling observational inverse prediction tasks within Giant Molecular Clouds (GMCs) for star formation. We introduce the Astro-DSB model, a variant of DSB with the pairwise domain assumption tailored for astrophysical dynamics. By investigating its learning process and prediction performance in both physically simulated data and in real observations (the Taurus B213 data), we present two main takeaways. First, from the astrophysical perspective, our proposed paired DSB method improves interpretability, learning efficiency, and prediction performance over conventional astrostatistical and other machine learning methods. Second, from the generative modeling perspective, probabilistic generative modeling reveals improvements over discriminative pixel-to-pixel modeling in Out-Of-Distribution (OOD) testing cases of physical simulations with unseen initial conditions and different dominant physical processes. Our study expands research into diffusion models beyond the traditional visual synthesis application and provides evidence of the models' learning abilities beyond pure data statistics, paving a path for future physics-aware generative models which can align dynamics between machine learning and real (astro)physical systems.

Generative models are spearheading recent progress in deep learning, showcasing strong promise for trajectory sampling in dynamical systems as well. However, whereas latent space modeling paradigms have transformed image and video generation, similar approaches are more difficult for most dynamical systems. Such systems -- from chemical molecule structures to collective human behavior -- are described by interactions of entities, making them inherently linked to connectivity patterns, entity conservation, and the traceability of entities over time. Our approach, LaM-SLidE (Latent Space Modeling of Spatial Dynamical Systems via Linked Entities), bridges the gap between: (1) keeping the traceability of individual entities in a latent system representation, and (2) leveraging the efficiency and scalability of recent advances in image and video generation, where pre-trained encoder and decoder enable generative modeling directly in latent space. The core idea of LaM-SLidE is the introduction of identifier representations (IDs) that enable the retrieval of entity properties and entity composition from latent system representations, thus fostering traceability. Experimentally, across different domains, we show that LaM-SLidE performs favorably in terms of speed, accuracy, and generalizability. Code is available at https://github.com/ml-jku/LaM-SLidE.

Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result, they are fundamentally ill-suited for applications involving inherently discrete quantities such as particle counts or material units, that are constrained by strict conservation laws like mass conservation, limiting their applicability in scientific workflows. To address this limitation, we propose Discrete Spatial Diffusion (DSD), a framework based on a continuous-time, discrete-state jump stochastic process that operates directly in discrete spatial domains while strictly preserving particle counts in both forward and reverse diffusion processes. By using spatial diffusion to achieve particle conservation, we introduce stochasticity naturally through a discrete formulation. We demonstrate the expressive flexibility of DSD by performing image synthesis, class conditioning, and image inpainting across standard image benchmarks, while exactly conditioning total image intensity. We validate DSD on two challenging scientific applications: porous rock microstructures and lithium-ion battery electrodes, demonstrating its ability to generate structurally realistic samples under strict mass conservation constraints, with quantitative evaluation using state-of-the-art metrics for transport and electrochemical performance.

Molecular representation learning has emerged as a promising approach for modeling molecules with deep learning in chemistry and beyond. While 3D geometric models effectively capture molecular structure, they typically process single static conformers, overlooking the inherent flexibility and dynamics of molecules. In reality, many molecular properties depend on distributions of thermodynamically accessible conformations rather than single structures. Recent works show that learning from conformer ensembles can improve molecular representations, but existing approaches either produce unphysical structures through averaging or require restrictive molecular alignment. In this paper, we propose SymmetryPreserving Conformer Ensemble networks (SPiCE), which introduces two key innovations: (1) geometric mixture-of-experts for selective processing of scalar and vector features, and (2) hierarchical ensemble encoding that combines ensemblelevel representation with cross-conformer integration. Crucially, SPiCE ensures physically meaningful representations by maintaining joint equivariance to geometric transformations of individual conformers and conformer permutations. Extensive experiments demonstrate that SPiCE consistently outperforms existing conformer ensemble methods and state-of-the-art structural aggregation models across quantum mechanical and biological property prediction tasks.

Periodicity, as one of the most important basic characteristics, lays the foundation for facilitating structured knowledge acquisition and systematic cognitive processes within human learning paradigms. However, the potential flaws of periodicity modeling in Transformer affect the learning efficiency and establishment of underlying principles from data for large language models (LLMs) built upon it. In this paper, we demonstrate that integrating effective periodicity modeling can improve the learning efficiency and performance of LLMs. We introduce FANformer, which adapts Fourier Analysis Network (FAN) into attention mechanism to achieve efficient periodicity modeling, by modifying the feature projection process of attention mechanism. Extensive experimental results on language modeling show that FANformer consistently outperforms Transformer when scaling up model size and training tokens, underscoring its superior learning efficiency. Our pretrained FANformer-1B exhibits marked improvements on downstream tasks compared to open-source LLMs with similar model parameters or training tokens. Moreover, we reveal that FANformer exhibits superior ability to learn and apply rules for reasoning compared to Transformer. The results position FANformer as an effective and promising architecture for advancing LLMs.

In this paper we introduce Hierarchical Diffusion Language Models (HDLM) -- a novel family of discrete diffusion models for language modeling. HDLM builds on a hierarchical vocabulary where low-level tokens with detailed semantics are surjectively mapped to high-level tokens with coarse-grained meanings. In the forward process, each token is independently perturbed to its higher-level ancestor with more abstract semantics according to the scheduler, while in the reverse process the model progressively predicts the next, more detailed semantics. Taken together, HDLM provides a general time-varying next semantic scale prediction process for language modeling. We derive closed-form expressions for the diffusion Evidence Lower Bound (ELBO), and show that HDLM can be implemented in a flexible manner while including the existing MDLM as a special case. We also propose practical training techniques based on the insights. Extensive text generation experiments validate the effectiveness of HDLM, which demonstrates consistently lower validation and generative perplexity than baselines.

Masked generative models (MGMs) have emerged as a powerful framework for image synthesis, combining parallel decoding with strong bidirectional context modeling. However, generating high-quality samples typically requires many iterative decoding steps, resulting in high inference costs. A straightforward way to speed up generation is by decoding more tokens in each step, thereby reducing the total number of steps. However, when many tokens are decoded simultaneously, the model can only estimate the univariate marginal distributions independently, failing to capture the dependency among them. As a result, reducing the number of steps significantly compromises generation fidelity. In this work, we introduce ReCAP (Reused Context-Aware Prediction), a plug-and-play module that accelerates inference in MGMs by constructing low-cost steps via reusing feature embeddings from previously decoded context tokens. ReCAP interleaves standard full evaluations with lightweight steps that cache and reuse context features, substantially reducing computation while preserving the benefits of fine-grained, iterative generation. We demonstrate its effectiveness on top of three representative MGMs (MaskGIT, MAGE, and MAR), including both discrete and continuous token spaces and covering diverse architectural designs. In particular, on ImageNet256 class-conditional generation, ReCAP achieves up to 2.4$\times$ faster inference than the base model with minimal performance drop, and consistently delivers better efficiency–fidelity trade-offs under various generation settings.

Recent efficient sequence modeling methods, such as Gated DeltaNet, TTT, and RWKV-7, have achieved performance improvements by supervising the recurrent memory management through the Delta learning rule. Unlike previous state-space models (e.g., Mamba) and gated linear attentions (e.g., GLA), these models introduce interactions between the recurrent state and the key vector, resulting in a bilinear recursive structure. In this paper, we first introduce the concept of Bilinear RNNs with a comprehensive analysis on the advantages and limitations of these models. Then based on the closed-loop control theory, we propose a novel Bilinear RNN variant named Comba, which adopts a scalar-plus-low-rank state transition, with both state feedback and output feedback corrections. We also implement a hardware-efficient chunk-wise parallel kernel in Triton and train models with 340M/1.3B parameters on a large-scale corpus. Comba demonstrates its superior performance and computation efficiency on both language modeling and vision tasks.

Understanding protein dynamics is critical for elucidating their biological functions. The increasing availability of molecular dynamics (MD) data enables the training of deep generative models to efficiently explore the conformational space of proteins. However, existing approaches either fail to explicitly capture the temporal dependencies between conformations or do not support direct generation of time-independent samples. To address these limitations, we introduce *ConfRover*, an autoregressive model that simultaneously learns protein conformation and dynamics from MD trajectory data, supporting both time-dependent and time-independent sampling. At the core of our model is a modular architecture comprising: (i) an *encoding layer*, adapted from protein folding models, that embeds protein-specific information and conformation at each time frame into a latent space; (ii) a *temporal module*, a sequence model that captures conformational dynamics across frames; and (iii) an SE(3) diffusion model as the *structure decoder*, generating conformations in continuous space. Experiments on ATLAS, a large-scale protein MD dataset of diverse structures, demonstrate the effectiveness of our model in learning conformational dynamics and supporting a wide range of downstream tasks. *ConfRover* is the first model to sample both protein conformations and trajectories within a single framework, offering a novel and flexible approach for learning from protein MD data.