NeurIPS 2025 Papers

Diffusion models have shown remarkable abilities in generating realistic and high-quality images from text prompts. However, a trained model remains largely black-box; little do we know about the roles of its components in exhibiting a concept such as objects or styles. Recent works employ causal tracing to localize knowledge-storing layers in generative models without showing how other layers contribute to the target concept. In this work, we approach diffusion models' interpretability problem from a more general perspective and pose a question: \textit{``How do model components work jointly to demonstrate knowledge?''}. To answer this question, we decompose diffusion models using component attribution, systematically unveiling the importance of each component (specifically the model parameter) in generating a concept. The proposed framework, called \textbf{C}omponent \textbf{A}ttribution for \textbf{D}iffusion Model (CAD), discovers the localization of concept-inducing (positive) components, while interestingly uncovers another type of components that contribute negatively to generating a concept, which is missing in the previous knowledge localization work. Based on this holistic understanding of diffusion models, we present and empirically evaluate one utility of component attribution in controlling the generation process. Specifically, we introduce two fast, inference-time model editing algorithms, CAD-Erase and CAD-Amplify; in particular, CAD-Erase enables erasure and CAD-Amplify allows amplification of a generated concept by ablating the positive and negative components, respectively, while retaining knowledge of other concepts. Extensive experimental results validate the significance of both positive and negative components pinpointed by our framework, demonstrating the potential of providing a complete view of interpreting generative models.

Text-to-image diffusion models have gained widespread application across various domains, demonstrating remarkable creative potential. However, the strong generalization capabilities of diffusion models can inadvertently lead to the generation of not-safe-for-work (NSFW) content, posing significant risks to their safe deployment. While several concept erasure methods have been proposed to mitigate the issue associated with NSFW content, a comprehensive evaluation of their effectiveness across various scenarios remains absent. To bridge this gap, we introduce a full-pipeline toolkit specifically designed for concept erasure and conduct the first systematic study of NSFW concept erasure methods. By examining the interplay between the underlying mechanisms and empirical observations, we provide in-depth insights and practical guidance for the effective application of concept erasure methods in various real-world scenarios, with the aim of advancing the understanding of content safety in diffusion models and establishing a solid foundation for future research and development in this critical area.

Direct Preference Optimization (DPO) is a key framework for aligning text-to-image models with human preferences, extended by Stepwise Preference Optimization (SPO) to leverage intermediate steps for preference learning, generating more aesthetically pleasing images with significantly less computational cost. While effective, SPO's underlying mechanisms remain underexplored. In light of this, we critically re-examine SPO by formalizing its mechanism as gradient guidance. This new lens shows that SPO uses biased temporal weighting, giving too little weight to later generative steps, and unlike likelihood centric views it reveals substantial noise in the gradient estimates. Leveraging these insights, our GradSPO algorithm introduces a simplified loss and a targeted, variance-informed noise reduction strategy, enhancing training stability. Evaluations on SD 1.5 and SDXL show GradSPO substantially outperforms leading baselines in human preference, yielding images with markedly improved aesthetics and semantic faithfulness, leading to more robust alignment. Code and models are available at https://github.com/JoshuaTTJ/GradSPO.

In this work, we introduce TreeGen, a novel generative framework modeling distributions over hierarchies. We extend Bayesian Flow Networks (BFNs) to enable transitions between probabilistic and discrete hierarchies parametrized via categorical distributions. Our proposed scheduler provides smooth and consistent entropy decay across varying numbers of categories. We empirically evaluate TreeGen on the jet-clustering task in high-energy physics, demonstrating that it consistently generates valid trees that adhere to physical constraints and closely align with ground-truth log-likelihoods. Finally, by comparing TreeGen’s samples to the exact posterior distribution and performing likelihood maximization via rejection sampling, we demonstrate that TreeGen outperforms various baselines.

Solving inverse problems—recovering signals from incomplete or noisy measurements—is fundamental in science and engineering. Score-based generative models (SGMs) have recently emerged as a powerful framework for this task. Two main paradigms have formed: unsupervised approaches that adapt pretrained generative models to inverse problems, and supervised bridge methods that train stochastic processes conditioned on paired clean and corrupted data. While the former typically assume knowledge of the measurement model, the latter have largely overlooked this structural information. We introduce System-embedded Diffusion Bridge Models (SDBs), a new class of supervised bridge methods that explicitly embed the known linear measurement system into the coefficients of a matrix-valued SDE. This principled integration yields consistent improvements across diverse linear inverse problems and demonstrates robust generalization under system misspecification between training and deployment, offering a promising solution to real-world applications.

Changing facial expressions, gestures, or background details may dramatically alter the meaning conveyed by an image. Notably, recent advances in diffusion models greatly improve the quality of image manipulation while also opening the door to misuse. Identifying changes made to authentic images, thus, becomes an important task, constantly challenged by new diffusion-based editing tools. To this end, we propose a novel approach for ReliAble iDentification of inpainted AReas (RADAR). RADAR builds on existing foundation models and combines features from different image modalities. It also incorporates an auxiliary contrastive loss that helps to isolate manipulated image patches. We demonstrate these techniques to significantly improve both the accuracy of our method and its generalisation to a large number of diffusion models. To support realistic evaluation, we further introduce BBC-PAIR, a new comprehensive benchmark, with images tampered by 28 diffusion models. Our experiments show that RADAR achieves excellent results, outperforming the state-of-the-art in detecting and localising image edits made by both seen and unseen diffusion models. Further information about our code, data and models, including separate licensing terms, will be publicly available at https://alex-costanzino.github.io/radar/.

Deep generative models have recently been applied to physical systems governed by partial differential equations (PDEs), offering scalable simulation and uncertainty-aware inference. However, enforcing physical constraints, such as conservation laws (linear and nonlinear) and physical consistencies, remains challenging. Existing methods often rely on soft penalties or architectural biases that fail to guarantee hard constraints. In this work, we propose Physics-Constrained Flow Matching (PCFM), a zero-shot inference framework that enforces arbitrary nonlinear constraints in pretrained flow-based generative models. PCFM continuously guides the sampling process through physics-based corrections applied to intermediate solution states, while remaining aligned with the learned flow and satisfying physical constraints. Empirically, PCFM outperforms both unconstrained and constrained baselines on a range of PDEs, including those with shocks, discontinuities, and sharp features, while ensuring exact constraint satisfaction at the final solution. Our method provides a flexible framework for enforcing hard constraints in both scientific and general-purpose generative models, especially in applications where constraint satisfaction is essential.

Stochastic differential equations (SDEs) describe dynamical systems where deterministic flows, governed by a drift function, are superimposed with random fluctuations, dictated by a diffusion function. The accurate estimation (*or discovery*) of these functions from data is a central problem in machine learning, with wide application across the natural and social sciences. Yet current solutions either rely heavily on prior knowledge of the dynamics or involve intricate training procedures. We introduce FIM-SDE (Foundation Inference Model for SDEs), a pretrained recognition model that delivers accurate *in-context* (or zero-shot) estimation of the drift and diffusion functions of *low-dimensional* SDEs, from noisy time series data, and allows rapid *finetuning* to target datasets. Leveraging concepts from amortized inference and neural operators, we (pre)train FIM-SDE in a supervised fashion to map a large set of noisy, discretely observed SDE paths onto the space of drift and diffusion functions. We demonstrate that FIM-SDE achieves robust *in-context* function estimation across a wide range of synthetic and real-world processes --- from canonical SDE systems (*e.g*., double-well dynamics or weakly perturbed Lorenz attractors) to stock price recordings and oil-price and wind-speed fluctuations --- while matching the performance of symbolic, Gaussian process and Neural SDE baselines trained on the target datasets. When *finetuned* to the target processes, we show that FIM-SDE consistently outperforms all these baselines.

A fundamental challenge in organic chemistry is identifying and predicting the sequence of reactions that synthesize a desired target molecule. Due to the combinatorial nature of the chemical search space, single-step reactant prediction—i.e., single-step retrosynthesis—remains difficult, even for state-of-the-art template-free generative methods. These models often struggle to produce an accurate yet diverse set of feasible reactions in a chemically rational manner. In this paper, we propose RETRO SYNFLOW (RSF), a discrete flow-matching framework that formulates single-step retrosynthesis as a Markov bridge between a given product molecule and its corresponding reactants. Unlike prior approaches, RSF introduces a reaction center identification step to extract intermediate structures, or synthons, which serve as a more informative and structured source distribution for the discrete flow model. To further improve the diversity and chemical feasibility of generated samples, RSF incorporates Feynman-Kac (FK) steering with Sequential Monte Carlo (SMC) resampling at inference time. This approach leverages a learned forward-synthesis reward oracle to guide the generation process toward more promising reactant candidates. Empirically, RSF substantially outperforms the previous state-of-the-art methods in top-1 accuracy. In addition, FK-steering significantly improves round-trip accuracy, demonstrating stronger chemical validity and synthetic feasibility, all while maintaining competitive top-k performance. These results establish RSF as a new leading approach for single-step retrosynthesis prediction.

Vision-language-action (VLA) models provide a powerful approach to training control policies for physical systems, such as robots, by combining end-to-end learning with transfer of semantic knowledge from web-scale vision-language model (VLM) training. However, the constraints of real-time control are often at odds with the design of VLMs: the most powerful VLMs have tens or hundreds of billions of parameters, presenting an obstacle to real-time inference, and operate on discrete tokens rather than the continuous-valued outputs that are required for controlling robots. To address this challenge, recent VLA models have used specialized modules for efficient continuous control, such as action experts or continuous output heads, which typically require adding new untrained parameters to the pretrained VLM backbone. While these modules improve real-time and control capabilities, it remains an open question whether they preserve or degrade the semantic knowledge contained in the pretrained VLM, and what effect they have on the VLA training dynamics. In this paper, we study this question in the context of VLAs that include a continuous diffusion or flow matching action expert, showing that naively including such experts significantly harms both training speed and knowledge transfer. We provide an extensive analysis of various design choices, their impact on performance and knowledge transfer, and propose a technique for insulating the VLM backbone during VLA training that mitigates this issue. Videos are available at https://pi.website/research/knowledge_insulation and open-source model weights are available at https://github.com/Physical-Intelligence/openpi.

We introduce IntrinsiX, a novel method that generates high-quality intrinsic images from text description. In contrast to existing text-to-image models whose outputs contain baked-in scene lighting, our approach predicts physically-based rendering (PBR) maps. This enables the generated outputs to be used for content creation scenarios in core graphics applications that facilitate re-lighting, editing, and texture generation tasks. In order to train our generator, we exploit strong image priors, and pre-train separate models for each PBR material component (albedo, roughness, metallic, normals). We then align these models with a new cross-intrinsic attention formulation that concatenates key and value features in a consistent fashion. This allows us to exchange information between each output modality and to obtain semantically coherent PBR predictions. To ground each intrinsic component, we propose a rendering loss which provides image-space signals to constrain the model, thus facilitating sharp details also in the output BRDF properties. Our results demonstrate detailed intrinsic generation with strong generalization capabilities that outperforms existing intrinsic image decomposition methods used with generated images by a significant margin. Finally, we show a series of applications, including re-lighting, editing, and for the first time text-conditioned room-scale PBR texture generation. We will release the code and the pre-trained model weights.

Designing metal-organic frameworks (MOFs) with novel chemistries is a longstanding challenge due to their large combinatorial space and complex 3D arrangements of the building blocks. While recent deep generative models have enabled scalable MOF generation, they assume (1) a fixed set of building blocks and (2) known local 3D coordinates of building blocks. However, this limits their ability to (1) design novel MOFs and (2) generate the structure using novel building blocks. We propose a two-stage MOF generation framework that overcomes these limitations by modeling both chemical and geometric degrees of freedom. First, we train an SMILES-based autoregressive model to generate metal and organic building blocks, paired with a cheminformatics toolkit for 3D structure initialization. Second, we introduce a flow matching model that predicts translations, rotations, and torsional angles to assemble the blocks into valid 3D frameworks. Our experiments demonstrate improved reconstruction accuracy, the generation of valid, novel, and unique MOFs, and the ability to create novel building blocks. Our code is available at https://github.com/nayoung10/MOFFlow-2.

Predicting the 3D conformation of small molecules within protein binding sites is a key challenge in drug design. When a crystallized reference ligand (template) is available, it provides geometric priors that can guide 3D pose prediction. We present a two-stage method for ligand conformation generation guided by such templates. In the first stage, we introduce a molecular alignment approach based on flow-matching to generate 3D coordinates for the ligand, using the template structure as a reference. In the second stage, a differentiable pose optimization procedure refines this conformation based on shape and pharmacophore similarities, internal energy, and, optionally, the protein binding pocket. We introduce a new benchmark of ligand pairs co-crystallized with the same target to evaluate our approach and show that it outperforms standard docking tools and open-access alignment methods, especially in cases involving low similarity to the template or high ligand flexibility.

Diffusion models can be improved with additional guidance towards more effective representations of input. Indeed, prior empirical work has already shown that aligning internal representations of the diffusion model with those of pre-trained models improves generation quality. In this paper, we present a systematic framework for incorporating representation guidance into diffusion models. We provide alternative decompositions of denoising models along with their associated training criteria, where the decompositions determine when and how the auxiliary representations are incorporated. Guided by our theoretical insights, we introduce two new strategies for enhancing representation alignment in diffusion models. First, we pair examples with target representations either derived from themselves or arisen from different synthetic modalities, and subsequently learn a joint model over the multimodal pairs. Second, we design an optimal training curriculum that balances representation learning and data generation. Our experiments across image, protein sequence, and molecule generation tasks demonstrate superior performance as well as accelerated training. In particular, on the class-conditional ImageNet $256\times 256$ benchmark, our guidance results in $23.3$ times faster training than the original SiT-XL as well as four times speedup over the state-of-the-art method REPA.

Text-to-image diffusion models rely on text embeddings from a pre-trained text encoder, but these embeddings remain fixed across all diffusion timesteps, limiting their adaptability to the generative process. We propose Diffusion Adaptive Text Embedding (DATE), which dynamically updates text embeddings at each diffusion timestep based on intermediate perturbed data. We formulate an optimization problem and derive an update rule that refines the text embeddings at each sampling step to improve alignment and preference between the mean predicted image and the text. This allows DATE to dynamically adapts the text conditions to the reverse-diffused images throughout diffusion sampling without requiring additional model training. Through theoretical analysis and empirical results, we show that DATE maintains the generative capability of the model while providing superior text-image alignment over fixed text embeddings across various tasks, including multi-concept generation and text-guided image editing. Our code is available at https://github.com/aailab-kaist/DATE.

The remarkable progress in text-to-video diffusion models enables the generation of photorealistic videos, although the content of these generated videos often includes unnatural movement or deformation, reverse playback, and motionless scenes. Recently, an alignment problem has attracted huge attention, where we steer the output of diffusion models based on some measure of the content's goodness. Because there is a large room for improvement of perceptual quality along the frame direction, we should address which metrics we should optimize and how we can optimize them in the video generation. In this paper, we propose diffusion latent beam search with lookahead estimator, which can select a better diffusion latent to maximize a given alignment reward at inference time. We then point out that improving perceptual video quality with respect to alignment to prompts requires reward calibration by weighting existing metrics. This is because when humans or vision language models evaluate outputs, many previous metrics to quantify the naturalness of video do not always correlate with the evaluation. We demonstrate that our method improves the perceptual quality evaluated on the calibrated reward, VLMs, and human assessment, without model parameter update, and outputs the best generation compared to greedy search and best-of-N sampling under much more efficient computational cost. The experiments highlight that our method is beneficial to many capable generative models, and provide a practical guideline: we should prioritize the inference-time compute allocation into enabling the lookahead estimator and increasing the search budget, rather than expanding the denoising steps.

Dataset distillation seeks to condense datasets into smaller but highly representative synthetic samples. While diffusion models now lead all generative benchmarks, current distillation methods avoid them and rely instead on GANs or autoencoders, or, at best, sampling from a fixed diffusion prior. This trend arises because naive backpropagation through the long denoising chain leads to vanishing gradients, which prevents effective synthetic sample optimization. To address this limitation, we introduce Latent Dataset Distillation with Diffusion Models (LD3M), the first method to learn gradient-based distilled latents and class embeddings end-to-end through a pre-trained latent diffusion model. A linearly decaying skip connection, injected from the initial noisy state into every reverse step, preserves the gradient signal across dozens of timesteps without requiring diffusion weight fine-tuning. Across multiple ImageNet subsets at $128\times128$ and $256\times256$, LD3M improves downstream accuracy by up to 4.8 percentage points (1 IPC) and 4.2 points (10 IPC) over the prior state-of-the-art. The code for LD3M is provided at https://github.com/Brian-Moser/prune_and_distill.

Understanding visual scenes is fundamental to human intelligence. While discriminative models have significantly advanced computer vision, they often struggle with compositional understanding. In contrast, recent generative text-to-image diffusion models excel at synthesizing complex scenes, suggesting inherent compositional capabilities. Building on this, zero-shot diffusion classifiers have been proposed to repurpose diffusion models for discriminative tasks. While prior work offered promising results in discriminative compositional scenarios, these results remain preliminary due to a small number of benchmarks and a relatively shallow analysis of conditions under which the models succeed. To address this, we present a comprehensive study of the discriminative capabilities of diffusion classifiers on a wide range of compositional tasks. Specifically, our study covers three diffusion models (SD 1.5, 2.0, and, for the first time, 3-m) spanning 10 datasets and over 30 tasks. Further, we shed light on the role that target dataset domains play in respective performance; to isolate the domain effects, we introduce a new diagnostic benchmark \textsc{Self-Bench} comprised of images created by diffusion models themselves. Finally, we explore the importance of timestep weighting and uncover a relationship between domain gap and timestep sensitivity, particularly for SD3-m. To sum up, diffusion classifiers understand compositionality, but conditions apply! Code and dataset are available at https://github.com/eugene6923/Diffusion-Classifiers-Compositionality

The Schrödinger Bridge (SB) problem has become a fundamental tool in computational optimal transport and generative modeling. To address this problem, ideal methods such as Iterative Proportional Fitting and Iterative Markovian Fitting (IMF) have been proposed—alongside practical approximations like Diffusion Schrödinger Bridge and its Matching (DSBM) variant. While previous work have established asymptotic convergence guarantees for IMF, a quantitative, non-asymptotic understanding remains unknown. In this paper, we provide the first non-asymptotic exponential convergence guarantees for IMF under mild structural assumptions on the reference measure and marginal distributions, assuming a sufficiently large time horizon. Our results encompass two key regimes: one where the marginals are log-concave, and another where they are weakly log-concave. The analysis relies on new contraction results for the Markovian projection operator and paves the way to theoretical guarantees for DSBM.