NeurIPS 2025 Papers

Geometric molecule generative models have found expanding applications across various scientific domains, but their generation inefficiency has become a critical bottleneck. Through a systematic investigation of the generative trajectory, we discover a unique challenge for molecule geometric graph generation: generative models require determining the permutation order of atoms in the molecule before refining its atomic feature values. Based on this insight, we decompose the generation process into permutation phase and adjustment phase, and propose a geometric-informed prior and consistency parameter objective to accelerate each phase. Extensive experiments demonstrate that our approach achieves competitive performance with approximately 10 sampling steps, 7.5 × faster than previous state-of-the-art models and approximately 100 × faster than diffusion-based models, offering a significant step towards scalable molecular generation.

Existing video generation models excel at producing photo-realistic videos from text or images, but often lack physical plausibility and 3D controllability. To overcome these limitations, we introduce PhysCtrl, a novel framework for physics-grounded image-to-video generation with physical parameters and force control. At its core is a generative physics network that learns the distribution of physical dynamics across four materials (elastic, sand, plasticine, and rigid) via a diffusion model conditioned on physics parameters and applied forces. We represent physical dynamics as 3D point trajectories and train on a large-scale synthetic dataset of 550K animations generated by physics simulators. We enhance the diffusion model with a novel spatiotemporal attention block that emulates particle interactions and incorporates physics-based constraints during training to enforce physical plausibility. Experiments show that PhysCtrl generates realistic, physics-grounded motion trajectories which, when used to drive image-to-video models, yield high-fidelity, controllable videos that outperform existing methods in both visual quality and physical plausibility. Our code, model and data will be made publicly available upon publication.

How should we evaluate the quality of generative models? Many existing metrics focus on a model's producibility, i.e. the quality and breadth of outputs it can generate. However, the actual value from using a generative model stems not just from what it can produce but whether a user with a specific goal can produce an output that satisfies that goal. We refer to this property as steerability. In this paper, we first introduce a mathematical decomposition for quantifying steerability independently from producibility. Steerability is more challenging to evaluate than producibility because it requires knowing a user's goals. We address this issue by creating a benchmark task that relies on one key idea: sample an output from a generative model and ask users to reproduce it. We implement this benchmark in user studies of text-to-image and large language models. Despite the ability of these models to produce high-quality outputs, they all perform poorly on steerability. These results suggest that we need to focus on improving the steerability of generative models. We show such improvements are indeed possible: simple image-based steering mechanisms achieve more than 2x improvement on this benchmark.

While diffusion models have shown promise for combinatorial optimization (CO), their inference-time scaling cost-efficiency remains relatively underexplored. Existing methods improve solution quality by increasing denoising steps, but the performance often becomes saturated quickly. This paper proposes GenSCO to systematically scale diffusion solvers by an orthogonal dimension of inference-time computation beyond denoising step expansion, i.e., search-driven generation. GenSCO takes generation as a search operator rather than a complete solving process, where each operator cycle combines solution disruption (via local search operators) and diffusion sampling, enabling iterative exploration of the learned solution space. Rather than over-refining current solutions, this paradigm encourages the model to leave local optima and explore a broader area of the solution space, ensuring a more consistent scaling effect. The search loop is supported by a search-friendly solution-enhancement training procedure that incorporates a rectified flow model learning to establish diffusion trajectories between suboptimal solutions and the optimal ones. The flow model is empowered by a lightweight transformer architecture to learn neural ODEs that linearize solution trajectories, accelerating convergence of the scaling effect with efficiency. The resulting enhanced scaling efficiency and practical scalability lead to synergistic performance improvements. Extensive experiments show that GenSCO delivers performance improvements by orders of magnitude over previous state-of-the-art neural methods. Notably, GenSCO even achieves significant speedups compared to the state-of-the-art classic mathematical solver LKH3, delivering a 141x speedup to reach 0.000% optimality gap on TSP-100, and approximately a 10x speedup to reach 0.02% on TSP-500.

3D human motion-text retrieval is essential for accurate motion understanding, targeted at cross-modal alignment learning. Existing methods typically align the global motion-text concepts directly, suffering from sub-optimal generalization due to the uncertainty of correspondence learning between multiple motion concepts coupled in a single motion/text sequence. Therefore, we study the explicit fine-grained concept decomposition for alignment learning and present a novel framework, Structural Generative Augmentation for 3D Human Motion Retrieval (SGAR), to enable generation-augmented retrieval. Specifically, relying on the strong priors of existing large language model (LLM) assets, we effectively decompose human motions structurally into subtler semantic units, \ie, body parts, for fine-grained motion modeling. Based on this, we develop part-mixture learning to better decouple the local motion concept learning, boosting part-level alignment. Moreover, a directional relation alignment strategy exploiting the correspondence between full-body and part motions is incorporated to regularize feature manifold for better consistency. Extensive experiments on three benchmarks, including motion-text retrieval as well as recognition and generation applications, demonstrate the superior performance and promising transferability of our method.

Concavity and its refinements underpin tractability in multiplayer games, where players independently choose actions to maximize their own payoffs which depend on other players’ actions. In *concave* games, where players' strategy sets are compact and convex, and their payoffs are concave in their own actions, strong guarantees follow: Nash equilibria always exist and decentralized algorithms converge to equilibria. If the game is furthermore *monotone*, an even stronger guarantee holds: Nash equilibria are unique under strictness assumptions. Unfortunately, we show that *certifying* concavity or monotonicity is NP-hard, already for games where utilities are multivariate polynomials and compact, convex basic semialgebraic strategy sets—an expressive class that captures extensive-form games with imperfect recall. On the positive side, we develop two hierarchies of sum-of-squares programs that certify concavity and monotonicity of a given game, and each level of the hierarchies can be solved in polynomial time. We show that almost all concave/monotone games are certified at some finite level of the hierarchies. Subsequently, we introduce the classes of SOS-concave/monotone games, which globally approximate concave/monotone games, and show that for any given game we can compute the closest SOS-concave/monotone game in polynomial time. Finally, we apply our techniques to canonical examples of extensive-form games with imperfect recall.

Conformational ensembles of protein structures are immensely important both for understanding protein function and drug discovery in novel modalities such as cryptic pockets. Current techniques for sampling ensembles such as molecular dynamics (MD) are computationally inefficient, while many recent machine learning methods do not transfer to systems outside their training data. We propose JAMUN which performs MD in a smoothed, noised space of all-atom 3D conformations of molecules by utilizing the framework of walk-jump sampling. JAMUN enables ensemble generation for small peptides at rates of an order of magnitude faster than traditional molecular dynamics. The physical priors in JAMUN enables transferability to systems outside of its training data, even to peptides that are longer than those originally trained on. Our model, code and weights are available at https://github.com/prescient-design/jamun.

The ability to capture rich representations of combinatorial structures has enabled the application of machine learning to tasks such as analysis and generation of floorplans, terrains, images, and animations. Recent work has primarily focused on understanding structures with well-defined features, neighborhoods, or underlying distance metrics, while those lacking such characteristics remain largely unstudied. Examples of these combinatorial structures can be found in polygons, where a small change in the vertex locations causes a significant rearrangement of the combinatorial structure, expressed as a visibility or triangulation graphs. Current representation learning approaches fail to capture structures without well-defined features and distance metrics. In this paper, we study the open problem of Visibility Reconstruction: Given a visibility graph $G$, construct a polygon $P$ whose visibility graph is $G$. We introduce $\textbf{VisDiff}$, a novel diffusion-based approach to generate polygon $P$ from the input visibility graph $G$. The main novelty of our approach is that, rather than generating the polygon's vertex set directly, we first estimate the signed distance function (SDF) associated with the polygon. The SDF is then used to extract the vertex location representing the final polygon. We show that going through the SDF allows $\textbf{VisDiff}$ to learn the visibility relationship much more effectively than generating vertex locations directly. In order to train $\textbf{VisDiff}$, we create a carefully curated dataset. We use this dataset to benchmark our method and achieve 26\% improvement in F1-Score over standard methods as well as state of the art approaches. We also provide preliminary results on the harder visibility graph recognition problem in which the input $G$ is not guaranteed to be a visibility graph. To demonstrate the applicability of VisDiff beyond visibility graphs, we extend it to the related combinatorial structure of triangulation graph. Lastly, leveraging these capabilties, we show that VisDiff can perform high-diversity sampling over the space of all polygons. In particular, we highlight its ability to perform both polygon-to-polygon interpolation and graph-to-graph interpolation, enabling diverse sampling across the polygon space.

Generative modeling, representation learning, and classification are three core problems in machine learning (ML), yet their state-of-the-art (SoTA) solutions remain largely disjoint. In this paper, we ask: Can a unified principle address all three? Such unification could simplify ML pipelines and foster greater synergy across tasks. We introduce Latent Zoning Network (LZN) as a step toward this goal. At its core, LZN creates a shared Gaussian latent space that encodes information across all tasks. Each data type (e.g., images, text, labels) is equipped with an encoder that maps samples to disjoint latent zones, and a decoder that maps latents back to data. ML tasks are expressed as compositions of these encoders and decoders: for example, label-conditional image generation uses a label encoder and image decoder; image embedding uses an image encoder; classification uses an image encoder and label decoder. We demonstrate the promise of LZN in three increasingly complex scenarios: (1) LZN can enhance existing models (image generation): When combined with the SoTA Rectified Flow model, LZN improves FID on CIFAR10 from 2.76 to 2.59—without modifying the training objective. (2) LZN can solve tasks independently (representation learning): LZN can implement unsupervised representation learning without auxiliary loss functions, outperforming the seminal MoCo and SimCLR methods by 9.3% and 0.2%, respectively, on downstream linear classification on ImageNet. (3) LZN can solve multiple tasks simultaneously (joint generation and classification): With image and label encoders/decoders, LZN performs both tasks jointly by design, improving FID and achieving SoTA classification accuracy on CIFAR10. The code and trained models are available at https://github.com/microsoft/latent-zoning-networks. The project website is at https://zinanlin.me/blogs/latent_zoning_networks.html.

The widespread use of diffusion models has led to an abundance of AI-generated data, raising concerns about model collapse---a phenomenon in which recursive iterations of training on synthetic data lead to performance degradation. Prior work primarily characterizes this collapse via variance shrinkage or distribution shift, but these perspectives miss practical manifestations of model collapse. This paper identifies a transition from generalization to memorization during model collapse in diffusion models, where models increasingly replicate training data instead of generating novel content during iterative training on synthetic samples. This transition is directly driven by the declining entropy of the synthetic training data produced in each training cycle, which serves as a clear indicator of model degradation. Motivated by this insight, we propose an entropy-based data selection strategy to mitigate the transition from generalization to memorization and alleviate model collapse. Empirical results show that our approach significantly enhances visual quality and diversity in recursive generation, effectively preventing collapse.

We introduce RFMPose, a novel generative framework for category-level 6D object pose estimation that learns deterministic pose trajectories through Riemannian Flow Matching (RFM). Existing discriminative approaches struggle with multi-hypothesis predictions (e.g., symmetry ambiguities) and often require specialized network architectures. RFMPose advances this paradigm through three key innovations: (1) Ensuring geometric consistency via geodesic interpolation on Riemannian manifolds combined with bi-invariant metric constraints; (2) Alleviating symmetry-induced ambiguities through Riemannian Optimal Transport for probability mass redistribution without ad-hoc design; (3) Enabling end-to-end likelihood estimation through Hutchinson trace approximation, thereby eliminating auxiliary model dependencies. Extensive experiments on the Omni6DPose demonstrate state-of-the-art performance of the proposed method, with significant improvements of $\textbf{+4.1}$ in $\mathrm{\textbf{IoU}_{25}}$ and $\textbf{+2.4}$ in $\textbf{5°2cm}$ metrics compared to prior generative approaches. Furthermore, the proposed RFM framework exhibits robust sim-to-real transfer capabilities and facilitates pose tracking extensions with minimal architectural adaptation.

Diffusion models have emerged as powerful tools for generative tasks, producing high-quality outputs across diverse domains. However, how the generated data responds to the initial noise perturbation in diffusion models remains under-explored, hindering a deeper understanding of the controllability of the sampling process. In this work, we first observe an interesting phenomenon: the relationship between the change of generation outputs and the scale of initial noise perturbation is highly linear through the diffusion ODE sampling process. We then provide both theoretical and empirical analyses to justify this linearity property of the input–output (noise → generation data) relationship. Inspired by these insights, we propose a novel **C**ontrollable and **C**onstrained **S**ampling (CCS) method, along with a new controller algorithm for diffusion models, that enables precise control over both (1) the proximity of individual samples to a target image and (2) the alignment of the sample mean with the target, while preserving high sample quality. We conduct extensive experiments comparing our proposed sampling approach with other methods in terms of both sampling controllability and generated data quality. Results show that CCS achieves significantly more precise controllability while maintaining superior sample quality and diversity, enabling practical applications such as fine-grained and robust image editing. Code: [https://github.com/efzero/diffusioncontroller](https://github.com/efzero/diffusioncontroller)

We introduce FAEclust, a novel functional autoencoder framework for cluster analysis of multi-dimensional functional data, data that are random realizations of vector-valued random functions. Our framework features a universal-approximator encoder that captures complex nonlinear interdependencies among component functions, and a universal-approximator decoder capable of accurately reconstructing both Euclidean and manifold-valued functional data. Stability and robustness are enhanced through innovative regularization strategies applied to functional weights and biases. Additionally, we incorporate a clustering loss into the network's training objective, promoting the learning of latent representations that are conducive to effective clustering. A key innovation is our shape-informed clustering objective, ensuring that the clustering results are resistant to phase variations in the functions. We establish the universal approximation property of our non-linear decoder and validate the effectiveness of our model through extensive experiments.

Discrete diffusion models enable parallel token sampling for faster inference than autoregressive approaches. However, prior diffusion models use a decoder-only architecture, which requires sampling algorithms that invoke the full network at every denoising step and incur high computational cost. Our key insight is that discrete diffusion models perform two types of computation: 1) representing clean tokens and 2) denoising corrupted tokens, which enables us to use separate modules for each task. We propose an encoder-decoder architecture to accelerate discrete diffusion inference, which relies on an encoder to represent clean tokens and a lightweight decoder to iteratively refine a noised sequence. We also show that this architecture enables faster training of block diffusion models, which partition sequences into blocks for better quality and are commonly used in diffusion language model inference. We introduce a framework for **E**fficient **E**ncoder-**D**ecoder **D**iffusion (E2D2), consisting of an architecture with specialized training and sampling algorithms, and we show that E2D2 achieves superior trade-offs between generation quality and inference throughput on summarization, translation, and mathematical reasoning tasks.

Modeling and reconstructing multidimensional physical dynamics from sparse and off-grid observations presents a fundamental challenge in scientific research. Recently, diffusion-based generative modeling shows promising potential for physical simulation. However, current approaches typically operate on on-grid data with preset spatiotemporal resolution, but struggle with the sparsely observed and continuous nature of real-world physical dynamics. To fill the gaps, we present SDIFT, Sequential DIffusion in Functional Tucker space, a novel framework that generates full-field evolution of physical dynamics from irregular sparse observations. SDIFT leverages the functional Tucker model as the latent space representer with proven universal approximation property, and represents sparse observations as latent functions and Tucker core sequences. We then construct a sequential diffusion model with temporally augmented UNet in the functional Tucker space, denoising noise drawn from a Gaussian process to generate the sequence of core tensors. At the posterior sampling stage, we propose a Message-Passing Posterior Sampling mechanism, enabling conditional generation of the entire sequence guided by observations at limited time steps. We validate SDIFT on three physical systems spanning astronomical (supernova explosions, light-year scale), environmental (ocean sound speed fields, kilometer scale), and molecular (organic liquid, millimeter scale) domains, demonstrating significant improvements in both reconstruction accuracy and computational efficiency compared to state-of-the-art approaches.

In this manuscript, we analyze a solvable model of flow or diffusion-based generative model. We consider the problem of learning a model parametrized by a two-layer auto-encoder, trained with online stochastic gradient descent, on a high-dimensional target density with an underlying low-dimensional manifold structure. We derive a tight asymptotic characterization of low-dimensional projections of the distribution of samples generated by the learned model, ascertaining in particular its dependence on the number of training samples. Building on this analysis, we discuss how mode collapse can arise, and lead to model collapse when the generative model is re-trained on generated synthetic data.

In this work we consider generic Gaussian Multi-index models, in which the labels only depend on the (Gaussian) $d$-dimensional inputs through their projection onto a low-dimensional $r = O_d(1)$ subspace, and we study efficient agnostic estimation procedures for this hidden subspace. We introduce the *generative leap* exponent, a natural extension of the generative exponent from Damian et al. 2024 to the multi-index setting. We show that a sample complexity of $n=\Theta(d^{1 \vee k^\star/2})$ is necessary in the class of algorithms captured by the Low-Degree-Polynomial framework; and also sufficient, by giving a sequential estimation procedure based on a spectral U-statistic over appropriate Hermite tensors.

Label distribution in recent years has been applied in a diverse array of complex decision-making tasks. To address the availability of label distributions, label enhancement has been established as an effective learning paradigm that aims to automatically infer label distributions from readily available multi-label data, e.g., logical labels. Recently, numerous works have demonstrated that the label ranking is significantly beneficial to label enhancement. However, these works still exhibit deficiencies in representing the probabilistic relationships between label distribution and label rankings, or fail to accommodate scenarios where multiple labels are equally important for a given instance. Therefore, we propose PROM, a pairwise ranking model with orderliness and monotonicity, to explain the probabilistic relationship between label distributions and label rankings. Specifically, we propose the monotonicity and orderliness assumptions for the probabilities of different ranking relationships and derive the mass functions for PROM, which are theoretically ensured to preserve the monotonicity and orderliness. Further, we propose a generative label enhancement algorithm based on PROM, which directly learns a label distribution predictor from the readily available multi-label data. Finally, extensive experiments demonstrate the efficacy of our proposed model.

Large language models (LLMs) have shown that generative pretraining can distill vast world knowledge into compact token representations. While LLMs encapsulate extensive world knowledge, they remain limited in modeling the behavioral knowledge contained within user interaction histories. User behavior forms a distinct modality, where each action—defined by multi-dimensional attributes such as time, context, and transaction type—constitutes a behavioral token. Modeling these high-cardinality, sparse, and irregular sequences is challenging, and discriminative models often falter under limited supervision. To bridge this gap, we extend generative pretraining to user behavior, learning transferable representations from unlabeled behavioral data analogous to how LLMs learn from text. We present PANTHER, a hybrid generative–discriminative framework that unifies user behavior pretraining and downstream adaptation, enabling large-scale sequential user representation learning and real-time inference. PANTHER introduces: (1) Structured Tokenization to compress multi-dimensional transaction attributes into an interpretable vocabulary; (2) Sequence Pattern Recognition Module (SPRM) for modeling periodic transaction motifs; (3) a Unified User-Profile Embedding that fuses static demographics with dynamic transaction histories, enabling both personalized predictions and population-level knowledge transfer; and (4) Real-time scalability enabled by offline caching of pre-trained embeddings for millisecond-level inference.Fully deployed and operational online at WeChat Pay, PANTHER delivers a 25.6\% boost in next-transaction prediction HitRate@1 and a 38.6\% relative improvement in fraud detection recall over baselines. Cross-domain evaluations on public benchmarks (CCT, MBD, MovieLens-1M, Yelp) show strong generalization, achieving up to 21\% HitRate@1 gains over transformer baselines, establishing PANTHER as a scalable, high-performance framework for industrial user sequential behavior modeling.