ICML 2025 Papers

We derive a controlled generation objective within the framework of Variational Flow Matching (VFM), which casts flow matching as a variational inference problem. We demonstrate that controlled generation can be implemented two ways: (1) by way of end-to-end training of conditional generative models, or (2) as a Bayesian inference problem, enabling post hoc control of unconditional models without retraining. Furthermore, we establish the conditions required for equivariant generation and provide an equivariant formulation of VFM tailored for molecular generation, ensuring invariance to rotations, translations, and permutations. We evaluate our approach on both uncontrolled and controlled molecular generation, achieving state-of-the-art performance on uncontrolled generation and outperforming state-of-the-art models in controlled generation, both with end-to-end training and in the Bayesian inference setting. This work strengthens the connection between flow-based generative modeling and Bayesian inference, offering a scalable and principled framework for constraint-driven and symmetry-aware generation.

Conditional diffusion and flow models are effective for super-resolving small-scale details in natural images. However, in physical sciences such as weather, three major challenges arise: (i) spatially misaligned input-output distributions (PDEs at different resolutions lead to divergent trajectories), (ii) misaligned and distinct input-output channels (channel synthesis), (iii) several channels with diverse stochasticity scales (multiscale). To address these, we propose to first encode inputs into a latent base distribution that is closer to the target, then apply Flow Matching to generate small-scale physics. The encoder captures deterministic components, while Flow Matching adds stochastic details. To handle uncertainty in the deterministic part, we inject noise via an adaptive noise scaling mechanism, dynamically adjusted by maximum-likelihood estimates of the encoder’s predictions. Experiments on real-world weather data (including super-resolution from 25 km to 2 km scales in Taiwan) and in synthetic Kolmogorov flow datasets show that our proposed Adaptive Flow Matching (AFM) framework outperforms existing methods and produces better-calibrated ensembles.

Reinforcement Learning (RL) optimizes Traffic Signal Control (TSC) to reduce congestion and emissions, but real-world TSC systems face challenges like adversarial attacks and missing data, leading to incorrect signal decisions and increased congestion. Existing methods, limited to offline data predictions, address only one issue and fail to meet TSC's dynamic, real-time needs. We propose RobustLight, a novel framework with an enhanced, plug-and-play diffusion model to improve TSC robustness against noise, missing data, and complex patterns by restoring attacked data. RobustLight integrates two algorithms to recover original data states without altering existing TSC platforms. Using a dynamic state infilling algorithm, it trains the diffusion model online. Experiments on real-world datasets show RobustLight improves recovery performance by up to 50.43\% compared to baseline scenarios. It effectively counters diverse adversarial attacks and missing data. The relevant datasets and code are available at Github.

We introduce a novel resampling criterion using lift scores, for improving compositional generation in diffusion models. By leveraging the lift scores, we evaluate whether generated samples align with each single condition and then compose the results to determine whether the composed prompt is satisfied. Our key insight is that lift scores can be efficiently approximated using only the original diffusion model, requiring no additional training or external modules. We develop an optimized variant that achieves relatively lower computational overhead during inference while maintaining effectiveness. Through extensive experiments, we demonstrate that lift scores significantly improved the condition alignment for compositional generation across 2D synthetic data, CLEVR position tasks, and text-to-image synthesis. Our code is available at github.com/rainorangelemon/complift.

Diffusion models have recently emerged as a powerful tool for planning. However, unlike Monte Carlo Tree Search (MCTS)—whose performance naturally improves with inference-time computation scaling—standard diffusion‐based planners offer only limited avenues for the scalability. In this paper, we introduce Monte Carlo Tree Diffusion (MCTD), a novel framework that integrates the generative strength of diffusion models with the adaptive search capabilities of MCTS. Our method reconceptualizes denoising as a tree‐structured process, allowing partially denoised plans to be iteratively evaluated, pruned, and refined. By selectively expanding promising trajectories while retaining the flexibility to revisit and improve suboptimal branches, MCTD achieves the benefits of MCTS such as controlling exploration-exploitation trade-offs within the diffusion framework. Empirical results on challenging long‐horizon tasks show that MCTD outperforms diffusion baselines, yielding higher‐quality solutions as inference-time computation increases.

Modern physics simulation often involves multiple functions of interests, and traditional numerical approaches are known to be complex and computationally costly. While machine learning-based surrogate models can offer significant cost reductions, most focus on a single task, such as forward prediction, and typically lack uncertainty quantification --- an essential component in many applications. To overcome these limitations, we propose Arbitrarily-Conditioned Multi-Functional Diffusion (ACM-FD), a versatile probabilistic surrogate model for multi-physics emulation. ACM-FD can perform a wide range of tasks within a single framework, including forward prediction, various inverse problems, and simulating data for entire systems or subsets of quantities conditioned on others. Specifically, we extend the standard Denoising Diffusion Probabilistic Model (DDPM) for multi-functional generation by modeling noise as Gaussian processes (GP). We propose a random-mask based, zero-regularized denoising loss to achieve flexible and robust conditional generation. We induce a Kronecker product structure in the GP covariance matrix, substantially reducing the computational cost and enabling efficient training and sampling. We demonstrate the effectiveness of ACM-FD across several fundamental multi-physics systems.

Diffusion models have shown great promise in decision-making, also known as diffusion planning. However, the slow inference speeds limit their potential for broader real-world applications. Here, we introduce **Habi**, a general framework that transforms powerful but slow diffusion planning models into fast decision-making models, which mimics the cognitive process in the brain that costly goal-directed behavior gradually transitions to efficient habitual behavior with repetitive practice. Even using a laptop CPU, the habitized model can achieve an average **800+ Hz** decision-making frequency (faster than previous diffusion planners by orders of magnitude) on standard offline reinforcement learning benchmarks D4RL, while maintaining comparable or even higher performance compared to its corresponding diffusion planner. Our work proposes a fresh perspective of leveraging powerful diffusion models for real-world decision-making tasks. We also provide robust evaluations and analysis, offering insights from both biological and engineering perspectives for efficient and effective decision-making.

The application of deep learning for partial differential equation (PDE)-constrained control is gaining increasing attention. However, existing methods rarely consider safety requirements crucial in real-world applications. To address this limitation, we propose Safe Diffusion Models for PDE Control (SafeDiffCon), which introduce the uncertainty quantile as model uncertainty quantification to achieve optimal control under safety constraints through both post-training and inference phases. Firstly, our approach post-trains a pre-trained diffusion model to generate control sequences that better satisfy safety constraints while achieving improved control objectives via a reweighted diffusion loss, which incorporates the uncertainty quantile estimated using conformal prediction. Secondly, during inference, the diffusion model dynamically adjusts both its generation process and parameters through iterative guidance and fine-tuning, conditioned on control targets while simultaneously integrating the estimated uncertainty quantile. We evaluate SafeDiffCon on three control tasks: 1D Burgers' equation, 2D incompressible fluid, and controlled nuclear fusion problem. Results demonstrate that SafeDiffCon is the only method that satisfies all safety constraints, whereas other classical and deep learning baselines fail. Furthermore, while adhering to safety constraints, SafeDiffCon achieves the best control performance. The code can be found at https://github.com/AI4Science-WestlakeU/safediffcon.

The adoption of text-to-image diffusion models raises concerns over reliability, drawing scrutiny under the lens of various metrics like calibration, fairness, or compute efficiency. We focus in this work on two issues that arise when deploying these models: a lack of diversity when prompting images, and a tendency to recreate images from the training set. To solve both problems, we propose a method that coaxes the sampled trajectories of pretrained diffusion models to land on images that fall outside of a reference set. We achieve this by adding repellency terms to the diffusion SDE throughout the generation trajectory, which are triggered whenever the path is expected to land too closely to an image in the shielded reference set. Our method is sparse in the sense that these repellency terms are zero and inactive most of the time, and even more so towards the end of the generation trajectory. Our method, named SPELL for sparse repellency, can be used either with a static reference set that contains protected images, or dynamically, by updating the set at each timestep with the expected images concurrently generated within a batch, and with the images of previously generated batches. We show that adding SPELL to popular diffusion models improves their diversity while impacting their FID only marginally, and performs comparatively better than other recent training-free diversity methods. We also demonstrate how SPELL can ensure a shielded generation away from a very large set of protected images by considering all 1.2M images from ImageNet as the protected set.

Recent diffusion-based generative models achieve remarkable results by training on massive datasets, yet this practice raises concerns about memorization and copyright infringement. A proposed remedy is to train exclusively on noisy data with potential copyright issues, ensuring the model never observes original content. However, through the lens of deconvolution theory, we show that although it is theoretically feasible to learn the data distribution from noisy samples, the practical challenge of collecting sufficient samples makes successful learning nearly unattainable. To overcome this limitation, we propose to pretrain the model with a small fraction of clean data to guide the deconvolution process. Combined with our Stochastic Forward--Backward Deconvolution (SFBD) method, we attain FID 6.31 on CIFAR-10 with just 4% clean images (and 3.58 with 10%). We also provide theoretical guarantees that SFBD learns the true data distribution. These results underscore the value of limited clean pretraining, or pretraining on similar datasets. Empirical studies further validate and enrich our findings.

Counterfactual image generation presents significant challenges, including preserving identity, maintaining perceptual quality, and ensuring faithfulness to an underlying causal model. While existing auto-encoding frameworks admit semantic latent spaces which can be manipulated for causal control, they struggle with scalability and fidelity. Advancements in diffusion models present opportunities for improving counterfactual image editing, having demonstrated state-of-the-art visual quality, human-aligned perception and representation learning capabilities. Here, we present a suite of diffusion-based causal mechanisms, introducing the notions of spatial, semantic and dynamic abduction. We propose a general framework that integrates semantic representations into diffusion models through the lens of Pearlian causality to edit images via a counterfactual reasoning process. To the best of our knowledge, ours is the first work to consider high-level semantic identity preservation for diffusion counterfactuals and to demonstrate how semantic control enables principled trade-offs between faithful causal control and identity preservation.

Shock waves caused by earthquakes can be devastating. Generating realistic earthquake-caused ground motion waveforms help reducing losses in lives and properties, yet generative models for the task tend to generate subpar waveforms. We present High-fidelity Earthquake Groundmotion Generation System (HEGGS) and demonstrate its superior performance using earthquakes from North American, East Asian, and European regions. HEGGS exploits the intrinsic characteristics of earthquake dataset and learns the waveforms using an end-to-end differentiable generator containing conditional latent diffusion model and hi-fidelity waveform construction model. We show the learning efficiency of HEGGS by training it on a single GPU machine and validate its performance using earthquake databases from North America, East Asia, and Europe, using diverse criteria from waveform generation tasks and seismology. Once trained, HEGGS can generate three dimensional E-N-Z seismic waveforms with accurate P/S phase arrivals, envelope correlation, signal-to-noise ratio, GMPE analysis, frequency content analysis, and section plot analysis.

While autoregressive models dominate natural language generation, their application to tabular data remains limited due to two challenges: 1) tabular data contains heterogeneous types, whereas autoregressive next-token (distribution) prediction is designed for discrete data, and 2) tabular data is column permutation-invariant, requiring flexible generation orders. Traditional autoregressive models, with their fixed generation order, struggle with tasks like missing data imputation, where the target and conditioning columns vary. To address these issues, we propose Diffusion-nested Non-autoregressive Transformer (TabNAT), a hybrid model combining diffusion processes and masked generative modeling. For continuous columns, TabNAT uses a diffusion model to parameterize their conditional distributions, while for discrete columns, it employs next-token prediction with KL divergence minimization. A masked Transformer with bi-directional attention enables order-agnostic generation, allowing it to learn the distribution of target columns conditioned on arbitrary observed columns. Extensive experiments on ten datasets with diverse properties demonstrate TabNAT's superiority in both unconditional tabular data generation and conditional missing data imputation tasks.

The practical applications of diffusion models have been limited by the misalignment between generated images and corresponding text prompts. Recent studies have introduced direct preference optimization (DPO) to enhance the alignment of these models. However, the effectiveness of DPO is constrained by the issue of visual inconsistency, where the significant visual disparity between well-aligned and poorly-aligned images prevents diffusion models from identifying which factors contribute positively to alignment during fine-tuning. To address this issue, this paper introduces D-Fusion, a method to construct DPO-trainable visually consistent samples. On one hand, by performing mask-guided self-attention fusion, the resulting images are not only well-aligned, but also visually consistent with given poorly-aligned images. On the other hand, D-Fusion can retain the denoising trajectories of the resulting images, which are essential for DPO training. Extensive experiments demonstrate the effectiveness of D-Fusion in improving prompt-image alignment when applied to different reinforcement learning algorithms.

Accuracy and speed are critical in image editing tasks. Pan et al. introduced a drag-based framework using Generative Adversarial Networks, and subsequent studies have leveraged large-scale diffusion models. However, these methods often require over a minute per edit and exhibit low success rates. We present LightningDrag, which achieves high-quality drag-based editing in about one second on general images. By redefining drag-based editing as a conditional generation task, we eliminate the need for time-consuming latent optimization or gradient-based guidance. Our model is trained on large-scale paired video frames, capturing diverse motion (object translations, pose shifts, zooming, etc.) to significantly improve accuracy and consistency. Despite being trained only on videos, our model generalizes to local deformations beyond the training data (e.g., lengthening hair, twisting rainbows). Extensive evaluations confirm the superiority of our approach, and we will release both code and model.

While diffusion models generate high-quality images via probability flow, the theoretical understanding of this process remains incomplete. A key question is when probability flow converges to training samples or more general points on the data manifold. We analyze this by studying the probability flow of shallow ReLU neural network denoisers trained with minimal $\ell^2$ norm. For intuition, we introduce a simpler score flow and show that for orthogonal datasets, both flows follow similar trajectories, converging to a training point or a sum of training points. However, early stopping by the diffusion time scheduler allows probability flow to reach more general manifold points. This reflects the tendency of diffusion models to both memorize training samples and generate novel points that combine aspects of multiple samples, motivating our study of such behavior in simplified settings. We extend these results to obtuse simplex data and, through simulations in the orthogonal case, confirm that probability flow converges to a training point, a sum of training points, or a manifold point. Moreover, memorization decreases when the number of training samples grows, as fewer samples accumulate near training points.

While score-based generative models are the model of choice across diverse domains, there are limited tools available for controlling inference-time behavior in a principled manner, e.g. for composing multiple pretrained models. Existing classifier-free guidance methods use a simple heuristic to mix conditional and unconditional scores to approximately sample from conditional distributions. However, such methods do not approximate the intermediate distributions, necessitating additional `corrector' steps. In this work, we provide an efficient and principled method for sampling from a sequence of annealed, geometric-averaged, or product distributions derived from pretrained score-based models. We derive a weighted simulation scheme which we call Feynman-Kac Correctors (FKCs) based on the celebrated Feynman-Kac formula by carefully accounting for terms in the appropriate partial differential equations (PDEs). To simulate these PDEs, we propose Sequential Monte Carlo (SMC) resampling algorithms that leverage inference-time scaling to improve sampling quality. We empirically demonstrate the utility of our methods by proposing amortized sampling via inference-time temperature annealing, improving multi-objective molecule generation using pretrained models, and improving classifier-free guidance for text-to-image generation.

Distribution matching (DM) is a versatile domain-invariant representation learning technique that has been applied to tasks such as fair classification, domain adaptation, and domain translation. Non-parametric DM methods struggle with scalability and adversarial DM approaches suffer from instability and mode collapse. While likelihood-based methods are a promising alternative, they often impose unnecessary biases through fixed priors or require explicit density models (e.g., flows) that can be challenging to train. We address this limitation by introducing a novel approach to training likelihood-based DM using expressive score-based prior distributions. Our key insight is that gradient-based DM training only requires the prior's score function---not its density---allowing us to train the prior via denoising score matching. This approach eliminates biases from fixed priors (e.g., in VAEs), enabling more effective use of geometry-preserving regularization, while avoiding the challenge of learning an explicit prior density model (e.g., a flow-based prior). Our method also demonstrates better stability and computational efficiency compared to other diffusion-based priors (e.g., LSGM). Furthermore, experiments demonstrate superior performance across multiple tasks, establishing our score-based method as a stable and effective approach to distribution matching. Source code available at https://github.com/inouye-lab/SAUB.

Flow and diffusion models have demonstrated strong performance and training stability across various tasks but lack two critical properties of simulation-based methods: freedom of dimensionality and adaptability to different inference trajectories. To address this limitation, we propose the Multidimensional Adaptive Coefficient (MAC), a plug-in module for flow and diffusion models that extends conventional unidimensional coefficients to multidimensional ones and enables inference trajectory-wise adaptation. MAC is trained via simulation-based feedback through adversarial refinement. Empirical results across diverse frameworks and datasets demonstrate that MAC enhances generative quality with high training efficiency. Consequently, our work offers a new perspective on inference trajectory optimality, encouraging future research to move beyond vector field design and to leverage training-efficient, simulation-based optimization.