ICML 2025 Papers

The Schrödinger Bridge (SB) is a powerful framework for solving generative modeling tasks such as unpaired domain translation. Most SB-related research focuses on continuous data space $\mathbb{R}^{D}$ and leaves open theoretical and algorithmic questions about applying SB methods to discrete data, e.g, on finite spaces $\mathbb{S}^{D}$. Notable examples of such sets $\mathbb{S}$ are codebooks of vector-quantized (VQ) representations of modern autoencoders, tokens in texts, categories of atoms in molecules, etc. In this paper, we provide a theoretical and algorithmic foundation for solving SB in discrete spaces using the recently introduced Iterative Markovian Fitting (IMF) procedure. Specifically, we theoretically justify the convergence of discrete-time IMF (D-IMF) to SB in discrete spaces. This enables us to develop a practical computational algorithm for SB, which we call Categorical Schrödinger Bridge Matching (CSBM). We show the performance of CSBM via a series of experiments with synthetic data and VQ representations of images. The code of CSBM is available at [this repository](https://github.com/gregkseno/csbm).

We introduce the Non-Equilibrium Transport Sampler (NETS), an algorithm for sampling from unnormalized probability distributions. NETS builds on non-equilibrium sampling strategies that transport a simple base distribution into the target distribution in finite time, as pioneered in Neal's annealed importance sampling (AIS). In the continuous-time setting, this transport is accomplished by evolving walkers using Langevin dynamics with a time-dependent potential, while simultaneously evolving importance weights to debias their solutions following Jarzynski's equality. The key innovation of NETS is to add to the dynamics a learned drift term that offsets the need for these corrective weights by minimizing their variance through an objective that can be estimated without backpropagation and provably bounds the Kullback-Leibler divergence between the estimated and target distributions. NETS provides unbiased samples and features a tunable diffusion coefficient that can be adjusted after training to maximize the effective sample size. In experiments on standard benchmarks, high-dimensional Gaussian mixtures, and statistical lattice field theory models, NETS shows compelling performances.

To circumvent the alignment of large language models (LLMs), current optimization-based adversarial attacks usually craft adversarial prompts by maximizing the likelihood of a so-called affirmative response. An affirmative response is a manually designed start of a harmful answer to an inappropriate request. While it is often easy to craft prompts that yield a substantial likelihood for the affirmative response, the attacked model frequently does not complete the response in a harmful manner. Moreover, the affirmative objective is usually not adapted to model-specific preferences and essentially ignores the fact that LLMs output a distribution over responses. If low attack success under such an objective is taken as a measure of robustness, the true robustness might be grossly overestimated. To alleviate these flaws, we propose an adaptive and semantic optimization problem over the population of responses. We derive a generally applicable objective via the REINFORCE policy-gradient formalism and demonstrate its efficacy with the state-of-the-art jailbreak algorithms Greedy Coordinate Gradient (GCG) and Projected Gradient Descent (PGD). For example, our objective doubles the attack success rate (ASR) on Llama3 and increases the ASR from 2\% to 50\% with circuit breaker defense.

Recovering human trajectories from incomplete or missing data is crucial for many mobility-based urban applications, e.g., urban planning, transportation, and location-based services. Existing methods mainly rely on recurrent neural networks or attention mechanisms. Though promising, they encounter limitations in capturing complex spatial-temporal dependencies in low-sampling trajectories. Recently, diffusion models show potential in content generation. However, most of proposed methods are used to generate contents in continuous numerical representations, which cannot be directly adapted to the human location trajectory recovery. In this paper, we introduce a conditional diffusion-based trajectory recovery method, namely, DiffMove. It first transforms locations in trajectories into the embedding space, in which the embedding denoising is performed, and then missing locations are recovered by an embedding decoder. DiffMove not only improves accuracy by introducing high-quality generative methods in the trajectory recovery, but also carefully models the transition, periodicity, and temporal patterns in human mobility. Extensive experiments based on two representative real-world mobility datasets are conducted, and the results show significant improvements (an average of 11% in recall) over the best baselines.

We study the theoretical foundations of composition in diffusion models, with a particular focus on out-of-distribution extrapolation and length-generalization. Prior work has shown that composing distributions via linear score combination can achieve promising results, including length-generalization in some cases (Du et al., 2023; Liu et al., 2022). However, our theoretical understanding of how and why such compositions work remains incomplete. In fact, it is not even entirely clear what it means for composition to "work". This paper starts to address these fundamental gaps. We begin by precisely defining one possible desired result of composition, which we call *projective composition*. Then, we investigate: (1) when linear score combinations provably achieve projective composition, (2) whether reverse-diffusion sampling can generate the desired composition, and (3) the conditions under which composition fails. We connect our theoretical analysis to prior empirical observations where composition has either worked or failed, for reasons that were unclear at the time. Finally, we propose a simple heuristic to help predict the success or failure of new compositions.

Constructing robust simulators is essential for asking "what if?" questions and guiding policy in critical domains like healthcare and logistics. However, existing methods often struggle, either failing to generalize beyond historical data or, when using Large Language Models (LLMs), suffering from inaccuracies and poor empirical alignment. We introduce **G-Sim**, a hybrid framework that automates simulator construction by synergizing LLM-driven structural design with rigorous empirical calibration. G-Sim employs an LLM in an iterative loop to propose and refine a simulator's core components and causal relationships, guided by domain knowledge. This structure is then grounded in reality by estimating its parameters using flexible calibration techniques. Specifically, G-Sim can leverage methods that are both **likelihood-free** and **gradient-free** with respect to the simulator, such as **gradient-free optimization** for direct parameter estimation or **simulation-based inference** for obtaining a posterior distribution over parameters. This allows it to handle non-differentiable and stochastic simulators. By integrating domain priors with empirical evidence, G-Sim produces reliable, causally-informed simulators, mitigating data-inefficiency and enabling robust system-level interventions for complex decision-making.

Spatial conditioning control offers a powerful way to guide diffusion‐based generative models. Yet, most implementations (e.g., ControlNet) rely on ad-hoc heuristics to choose which network blocks to control — an approach that varies unpredictably with different tasks. To address this gap, we propose FlexControl, a novel framework that equips all diffusion blocks with control signals during training and employs a trainable gating mechanism to dynamically select which control signal to activate at each denoising step. By introducing a computation-aware loss, we can encourage the control signal to activate only when it benefits the generation quality. By eliminating manual control unit selection, FlexControl enhances adaptability across diverse tasks and streamlines the design pipeline with computation-aware training loss in an end-to-end training manner. Through comprehensive experiments on both UNet and DiT architectures on different control methods, we show that our method can upgrade existing controllable generative models in certain key aspects of interest. As evidenced by both quantitative and qualitative evaluations, FlexControl preserves or enhances image fidelity while also reducing computational overhead by selectively activating the most relevant blocks to control. These results underscore the potential of a flexible, data‐driven approach for controlled diffusion and open new avenues for efficient generative model design. The code will soon be available at https://github.com/Daryu-Fan/FlexControl.

Image steganography ensures secure information transmission and storage by concealing secret messages within images. Recently, the diffusion model has been incorporated into the generative image steganography task, with text prompts being employed to guide the entire process. However, existing methods are plagued by three problems: (1) the restricted control exerted by text prompts causes generated stego images resemble the secret images and seem unnatural, raising the severe detection risk; (2) inconsistent intermediate states between Denoising Diffusion Implicit Models and its inversion, coupled with limited control of text prompts degrade the revealed secret images; (3) the descriptive text of images(i.e. text prompts) are also deployed as the keys, but this incurs significant security risks for both the keys and the secret images.To tackle these drawbacks, we systematically propose the SSHR, which joints the Reference Images with the adaptive keys to govern the entire process, enhancing the naturalness and imperceptibility of stego images. Additionally, we methodically construct an Exact Reveal Process to improve the quality of the revealed secret images. Furthermore, adaptive Reference-Secret Image Related Symmetric Keys are generated to enhance the security of both the keys and the concealed secret images. Various experiments indicate that our model outperforms existing methods in terms of recovery quality and secret image security.

The success of large generative models has driven a paradigm shift, leveraging massive multi-source data to enhance model capabilities. However, the interaction among these sources remains theoretically underexplored. This paper provides a first attempt to fill this gap by rigorously analyzing multi-source training in conditional generative modeling, where each condition represents a distinct data source. Specifically, we establish a general distribution estimation error bound in average total variation distance for conditional maximum likelihood estimation based on the bracketing number. Our result shows that when source distributions share certain similarities and the model is expressive enough, multi-source training guarantees a sharper bound than single-source training. We further instantiate the general theory on conditional Gaussian estimation and deep generative models including autoregressive and flexible energy-based models, by characterizing their bracketing numbers. The results highlight that the number of sources and similarity among source distributions improve the advantage of multi-source training. Simulations and real-world experiments validate our theory.

Diffusion transformers (DiT) have demonstrated exceptional performance in video generation. However, their large number of parameters and high computational complexity limit their deployment on edge devices. Quantization can reduce storage requirements and accelerate inference by lowering the bit-width of model parameters. Yet, existing quantization methods for image generation models do not generalize well to video generation tasks. We identify two primary challenges: the loss of information during quantization and the misalignment between optimization objectives and the unique requirements of video generation. To address these challenges, we present **Q-VDiT**, a quantization framework specifically designed for video DiT models. From the quantization perspective, we propose the *Token aware Quantization Estimator* (TQE), which compensates for quantization errors in both the token and feature dimensions. From the optimization perspective, we introduce *Temporal Maintenance Distillation* (TMD), which preserves the spatiotemporal correlations between frames and enables the optimization of each frame with respect to the overall video context. Our W3A6 Q-VDiT achieves a scene consistency score of 23.40, setting a new benchmark and outperforming the current state-of-the-art quantization methods by **1.9$\times$**.

Though typically represented by the discrete node and edge attributes, the graph topological information can be sufficiently captured by the graph spectrum in a continuous space. It is believed that incorporating the continuity of graph topological information into the generative process design could establish a superior paradigm for graph generative modeling. Motivated by such prior and recent advancements in the generative paradigm, we propose Graph Bayesian Flow Networks (GraphBFN) in this paper, a principled generative framework that designs an alternative generative process emphasizing the dynamics of topological information. Unlike recent discrete-diffusion-based methods, GraphBFNemploys the continuous counts derived from sampling infinite times from a categorical distribution as latent to facilitate a smooth decomposition of topological information, demonstrating enhanced effectiveness. To effectively realize the concept, we further develop an advanced sampling strategy and new time-scheduling techniques to overcome practical barriers and boost performance. Through extensive experimental validation on both generic graph and molecular graph generation tasks, GraphBFN could consistently achieve superior or competitive performance with significantly higher training and sampling efficiency.

While likelihood-based generative models, particularly diffusion and autoregressive models, have achieved remarkable fidelity in visual generation, the maximum likelihood estimation (MLE) objective, which minimizes the forward KL divergence, inherently suffers from a mode-covering tendency that limits the generation quality under limited model capacity. In this work, we propose Direct Discriminative Optimization (DDO) as a unified framework that integrates likelihood-based generative training and GAN-type discrimination to bypass this fundamental constraint by exploiting reverse KL and self-generated negative signals. Our key insight is to parameterize a discriminator implicitly using the likelihood ratio between a learnable target model and a fixed reference model, drawing parallels with the philosophy of Direct Preference Optimization (DPO). Unlike GANs, this parameterization eliminates the need for joint training of generator and discriminator networks, allowing for direct, efficient, and effective finetuning of a well-trained model to its full potential beyond the limits of MLE. DDO can be performed iteratively in a self-play manner for progressive model refinement, with each round requiring less than 1\% of pretraining epochs. Our experiments demonstrate the effectiveness of DDO by significantly advancing the previous SOTA diffusion model EDM, reducing FID scores from 1.79/1.58/1.96 to new records of 1.30/0.97/1.26 on CIFAR-10/ImageNet-64/ImageNet 512$\times$512 datasets without any guidance mechanisms, and by consistently improving both guidance-free and CFG-enhanced FIDs of visual autoregressive models on ImageNet 256$\times$256.

Generative image steganography (GIS) is an emerging technique that conceals secret messages in the generation of images. Compared to GAN-based or flow-based GIS schemes, diffusion model-based solutions can provide high-quality and more diverse images, thus receiving considerable attention recently. However, previous GIS schemes still face challenges in terms of extraction accuracy, controllability, and practicality. To address the above issues, this paper proposes a practical message-driven GIS framework based on diffusion models, called MDDM. Specifically, by utilizing Cardan Grille, we encode messages into Gaussian noise, which serves as the initial input for image generation, enabling users to generate diverse images via controllable prompts without additional training. During the information extraction process, receivers only need to use the pre-shared Cardan Grille to perform exact diffusion inversion and recover the messages without requiring the image generation seeds or prompts. Experimental results demonstrate that MDDM offers notable advantages in terms of accuracy, controllability, practicality, and security. With flexible strategies, MDDM can always achieve almost 100\% accuracy. Additionally, MDDM demonstrates certain robustness and exhibits potential for application in watermarking tasks.

Denoising diffusion probabilistic models (DDPMs) can be utilized to recover a clean signal from its degraded observation(s) by conditioning the model on the degraded signal. The degraded signals are themselves contaminated versions of the clean signals; due to this correlation, they may encompass certain useful information about the target clean data distribution. However, existing adoption of the standard Gaussian as the prior distribution in turn discards such information when shaping the prior, resulting in sub-optimal performance. In this paper, we propose to improve conditional DDPMs for signal restoration by leveraging a more informative prior that is jointly learned with the diffusion model. The proposed framework, called RestoreGrad, seamlessly integrates DDPMs into the variational autoencoder (VAE) framework, taking advantage of the correlation between the degraded and clean signals to encode a better diffusion prior. On speech and image restoration tasks, we show that RestoreGrad demonstrates faster convergence (5-10 times fewer training steps) to achieve better quality of restored signals over existing DDPM baselines and improved robustness to using fewer sampling steps in inference time (2-2.5 times fewer), advocating the advantages of leveraging jointly learned prior for efficiency improvements in the diffusion process.

Dataset distillation has emerged as an effective strategy, significantly reducing training costs and facilitating more efficient model deployment. Recent advances have leveraged generative models to distill datasets by capturing the underlying data distribution. Unfortunately, existing methods require model fine-tuning with distillation losses to encourage diversity and representativeness. However, these methods do not guarantee sample diversity, limiting their performance. We propose a mode-guided diffusion model leveraging a pre-trained diffusion model without the need to fine-tune with distillation losses. Our approach addresses dataset diversity in three stages: Mode Discovery to identify distinct data modes, Mode Guidance to enhance intra-class diversity, and Stop Guidance to mitigate artifacts in synthetic samples that affect performance. We evaluate our approach on ImageNette, ImageIDC, ImageNet-100, and ImageNet-1K, achieving accuracy improvements of 4.4%, 2.9%, 1.6%, and 1.6%, respectively, over state-of-the-art methods. Our method eliminates the need for fine-tuning diffusion models with distillation losses, significantly reducing computational costs.

Score-based generative models are essential in various machine learning applications, with strong capabilities in generation quality. In particular, high-order derivatives (scores) of data density offer deep insights into data distributions, building on the proven effectiveness of first-order scores for modeling and generating synthetic data, unlocking new possibilities for applications. However, learning them typically requires complete data, which is often unavailable in domains such as healthcare and finance due to data corruption, acquisition constraints, or incomplete records. To tackle this challenge, we introduce MissScore, a novel framework for estimating high-order scores in the presence of missing data. We derive objective functions for estimating high-order scores under different missing data mechanisms and propose a new algorithm specifically designed to handle missing data effectively. Our empirical results demonstrate that MissScore accurately and efficiently learns the high-order scores from incomplete data and generates high-quality samples, resulting in strong performance across a range of downstream tasks.

Diffusion-based generative models (diffusion models) often require a large amount of data to train a score-based model that learns the score function of the data distribution through denoising score matching. However, collecting and cleaning such data can be expensive, time-consuming, and even infeasible. In this paper, we present a novel theoretical insight for diffusion models that two factors, i.e., the denoiser function hypothesis space and the number of training samples, can affect the denoising score matching error of all training samples. Based on this theoretical insight, it is evident that minimizing the total denoising score matching error is challenging within the denoiser function hypothesis space in existing methods, when training diffusion models with limited data. To address this, we propose a new diffusion model called Limited Data Diffusion (LD-Diffusion), which consists of two main components: a compressing model and a novel mixed augmentation with fixed probability (MAFP) strategy. Specifically, the compressing model can constrain the complexity of the denoiser function hypothesis space and MAFP can effectively increase the training samples by providing more informative guidance than existing data augmentation methods in the compressed hypothesis space. Extensive experiments on several datasets demonstrate that LD-Diffusion can achieve better performance compared to other diffusion models. Codes are available at https://github.com/zzhang05/LD-Diffusion.

Visual tokenization via auto-encoding empowers state-of-the-art image and video generative models by compressing pixels into a latent space. However, questions remain about how auto-encoder design impacts reconstruction and downstream generative performance. This work explores scaling in auto-encoders for reconstruction and generation by replacing the convolutional backbone with an enhanced Vision Transformer for Tokenization (ViTok). We find scaling the auto-encoder bottleneck correlates with reconstruction but exhibits a nuanced relationship with generation. Separately, encoder scaling yields no gains, while decoder scaling improves reconstruction with minimal impact on generation. As a result, we determine that scaling the current paradigm of auto-encoders is not effective for improving generation performance. Coupled with Diffusion Transformers, ViTok achieves competitive image reconstruction and generation performance on 256p and 512p ImageNet-1K. In videos, ViTok achieves SOTA reconstruction and generation performance on 16-frame 128p UCF-101.

Generative modeling typically concerns transporting a single source distribution to a target distribution via simple probability flows. However, in fields like computer graphics and single-cell genomics, samples themselves can be viewed as distributions, where standard flow matching ignores their inherent geometry. We propose Wasserstein flow matching (WFM), which lifts flow matching onto families of distributions using the Wasserstein geometry. Notably, WFM is the first algorithm capable of generating distributions in high dimensions, whether represented analytically (as Gaussians) or empirically (as point-clouds). Our theoretical analysis establishes that Wasserstein geodesics constitute proper conditional flows over the space of distributions, making for a valid FM objective. Our algorithm leverages optimal transport theory and the attention mechanism, demonstrating versatility across computational regimes: exploiting closed-form optimal transport paths for Gaussian families, while using entropic estimates on point-clouds for general distributions. WFM successfully generates both 2D \& 3D shapes and high-dimensional cellular microenvironments from spatial transcriptomics data. Code is available at [WassersteinFlowMatching](https://github.com/WassersteinFlowMatching/WassersteinFlowMatching/).