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Deep Learning · Generative Models and Autoencoders

Gianluigi Silvestri, Luca Ambrogioni, Chieh-Hsin Lai, Yuhta Takida, Yuki Mitsufuji

Consistency Training (CT) has recently emerged as a strong alternative to diffusion models for image generation. However, non-distillation CT often suffers from high variance and instability, motivating ongoing research into its training dynamics. We propose Variational Consistency Training (VCT), a flexible and effective framework compatible with various forward kernels, including those in flow matching. Its key innovation is a learned noise-data coupling scheme inspired by Variational Autoencoders, where a data-dependent encoder models noise emission. This enables VCT to adaptively learn noise-to-data pairings, reducing training variance relative to the fixed, unsorted pairings in classical CT. Experiments on multiple image datasets demonstrate significant improvements: our method surpasses baselines, achieves state-of-the-art FID among non-distillation CT approaches on CIFAR-10, and matches SoTA performance on ImageNet 64x64 with only two sampling steps. Code is available at https://github.com/sony/vct.

Probabilistic Methods · Variational Inference

Junbin Liu, Farzan Farnia, Wing-Kin Ma

Multilayer matrix factorization (MMF) has recently emerged as a generalized model of, and potentially a more expressive approach than, the classic matrix factorization.This paper considers MMF under a probabilistic formulation, and our focus is on inference methods under variational inference.The challenge in this context lies in determining a variational process that leads to a computationally efficient and accurate approximation of the maximum likelihood inference. One well-known example is the variational autoencoder (VAE), which uses neural networks for the variational process.In this work, we take insight from variational diffusion models in the context of generative models to develop variational inference for MMF.We propose a dimension-reducing diffusion process that results in a new way to interact with the layered structures of the MMF model.Experimental results demonstrate that the proposed diffusion variational inference method leads to improved performance scores compared to several existing methods, including the VAE.

Deep Learning · Generative Models and Autoencoders

Jaeyeon Kim, Kulin Shah, Vasilis Kontonis, Sham Kakade, Sitan Chen

In recent years, masked diffusion models (MDMs) have emerged as a promising alternative approach for generative modeling over discrete domains. Compared to autoregressive models (ARMs), MDMs trade off complexity at training time with flexibility at inference time. At training time, they must learn to solve an exponentially large number of infilling problems, but at inference time, they can decode tokens in essentially arbitrary order. In this work we closely examine these two competing effects. On the training front, we theoretically and empirically demonstrate that MDMs indeed train on computationally intractable subproblems compared to their autoregressive counterparts. On the inference front, we show that a suitable strategy for adaptively choosing the token decoding order significantly enhances the capabilities of MDMs, allowing them to sidestep hard subproblems. On logic puzzles like Sudoku, we show that adaptive inference can boost solving accuracy in pretrained MDMs from $<7$\% to $\approx 90$\%, even outperforming ARMs that were explicitly trained via teacher forcing to learn the right order of decoding.

Deep Learning · Generative Models and Autoencoders

Cheng Jin, Zhenyu Xiao, Chutao Liu, Yuantao Gu

Classifier-free guidance (CFG) has emerged as a pivotal advancement in text-to-image latent diffusion models, establishing itself as a cornerstone technique for achieving high-quality image synthesis. However, under high guidance weights, where text-image alignment is significantly enhanced, CFG also leads to pronounced color distortions in the generated images. We identify that these distortions stem from the amplification of sample norms in the latent space. We present a theoretical framework that elucidates the mechanisms of norm amplification and anomalous diffusion phenomena induced by classifier-free guidance. Leveraging our theoretical insights and the latent space structure, we propose an Angle Domain Guidance (ADG) algorithm. ADG constrains magnitude variations while optimizing angular alignment, thereby mitigating color distortions while preserving the enhanced text-image alignment achieved at higher guidance weights. Experimental results demonstrate that ADG significantly outperforms existing methods, generating images that not only maintain superior text alignment but also exhibit improved color fidelity and better alignment with human perceptual preferences.

General Machine Learning

Riccardo De Santi, Marin Vlastelica, Ya-Ping Hsieh, Zebang Shen, Niao He, Andreas Krause

Exploration is critical for solving real-world decision-making problems such as scientific discovery, where the objective is to generate truly novel designs rather than mimic existing data distributions. In this work, we address the challenge of leveraging the representational power of generative models for exploration without relying on explicit uncertainty quantification. We introduce a novel framework that casts exploration as entropy maximization over the approximate data manifold implicitly defined by a pre-trained diffusion model. Then, we present a novel principle for exploration based on density estimation, a problem well-known to be challenging in practice. To overcome this issue and render this method truly scalable, we leverage a fundamental connection between the entropy of the density induced by a diffusion model and its score function. Building on this, we develop an algorithm based on mirror descent that solves the exploration problem as sequential fine-tuning of a pre-trained diffusion model. We prove its convergence to the optimal exploratory diffusion model under realistic assumptions by leveraging recent understanding of mirror flows. Finally, we empirically evaluate our approach on both synthetic and high-dimensional text-to-image diffusion, demonstrating promising results.

Deep Learning · Generative Models and Autoencoders

Yuchen Zhang, Jian Zhou

Inverse generation problems, such as denoising without ground truth observations, is a critical challenge in many scientific inquiries and real-world applications. While recent advances in generative models like diffusion models, conditional flow matching, and consistency models achieved impressive results by casting generation as denoising problems, they cannot be directly used for inverse generation without access to clean data. Here we introduce Inverse Flow (IF), a novel framework that enables using these generative models for inverse generation problems including denoising without ground truth. Inverse Flow can be flexibly applied to nearly any continuous noise distribution and allows complex dependencies. We propose two algorithms for learning Inverse Flows, Inverse Flow Matching (IFM) and Inverse Consistency Model (ICM). Notably, to derive the computationally efficient, simulation-free inverse consistency model objective, we generalized consistency training to any forward diffusion processes or conditional flows, which have applications beyond denoising. We demonstrate the effectiveness of IF on synthetic and real datasets, outperforming prior approaches while enabling noise distributions that previous methods cannot support. Finally, we showcase applications of our techniques to fluorescence microscopy and single-cell genomics data, highlighting IF's utility in scientific problems. Overall, this work expands the applications of powerful generative models to inversion generation problems.

Applications · Robotics

Zhendong Wang, Max Li, Ajay Mandlekar, Zhenjia Xu, Jiaojiao Fan, Yashraj Narang, Jim Fan, Yuke Zhu, Yogesh Balaji, Mingyuan Zhou 等

Diffusion models, praised for their success in generative tasks, are increasingly being applied to robotics, demonstrating exceptional performance in behavior cloning. However, their slow generation process stemming from iterative denoising steps poses a challenge for real-time applications in resource-constrained robotics setups and dynamically changing environments.In this paper, we introduce the One-Step Diffusion Policy (OneDP), a novel approach that distills knowledge from pre-trained diffusion policies into a single-step action generator, significantly accelerating response times for robotic control tasks. We ensure the distilled generator closely aligns with the original policy distribution by minimizing the Kullback-Leibler (KL) divergence along the diffusion chain, requiring only $2\%$-$10\%$ additional pre-training cost for convergence. We evaluated OneDP on 6 challenging simulation tasks as well as 4 self-designed real-world tasks using the Franka robot. The results demonstrate that OneDP not only achieves state-of-the-art success rates but also delivers an order-of-magnitude improvement in inference speed, boosting action prediction frequency from 1.5 Hz to 62 Hz, establishing its potential for dynamic and computationally constrained robotic applications. A video demo is provided at our project page, and the code will be publicly available.

Deep Learning · Generative Models and Autoencoders

Xiyue Zhu, Dou Kwark, Ruike Zhu, Kaiwen Hong, Yiqi Tao, Shirui Luo, Yudu Li, Zhi-Pei Liang, Volodymyr Kindratenko

In volume-to-volume translations in medical images, existing models often struggle to capture the inherent volumetric distribution using 3D voxel-space representations, due to high computational dataset demands. We present Score-Fusion, a novel volumetric translation model that effectively learns 3D representations by ensembling perpendicularly trained 2D diffusion models in score function space. By carefully initializing our model to start with an average of 2D models as in existing models, we reduce 3D training to a fine-tuning process, mitigating computational and data demands. Furthermore, we explicitly design the 3D model's hierarchical layers to learn ensembles of 2D features, further enhancing efficiency and performance. Moreover, Score-Fusion naturally extends to multi-modality settings by fusing diffusion models conditioned on different inputs for flexible, accurate integration. We demonstrate that 3D representation is essential for better performance in downstream recognition tasks, such as tumor segmentation, where most segmentation models are based on 3D representation. Extensive experiments demonstrate that Score-Fusion achieves superior accuracy and volumetric fidelity in 3D medical image super-resolution and modality translation. Additionally, we extend Score-Fusion to video super-resolution by integrating 2D diffusion models on time-space slices with a spatial-temporal video diffusion backbone, highlighting its potential for general-purpose volume translation and providing broader insight into learning-based approaches for score function fusion.

Theory · Deep Learning

Yujin Han, Andi Han, Wei Huang, Chaochao Lu, Difan Zou

Despite the remarkable success of diffusion models (DMs) in data generation, they exhibit specific failure cases with unsatisfactory outputs. We focus on one such limitation: the ability of DMs to learn hidden rules between image features. Specifically, for image data with dependent features ($\mathbf{x}$) and ($\mathbf{y}$) (e.g., the height of the sun ($\mathbf{x}$) and the length of the shadow ($\mathbf{y}$)), we investigate whether DMs can accurately capture the inter-feature rule ($p(\mathbf{y}|\mathbf{x})$). Empirical evaluations on mainstream DMs (e.g., Stable Diffusion 3.5) reveal consistent failures, such as inconsistent lighting-shadow relationships and mismatched object-mirror reflections. Inspired by these findings, we design four synthetic tasks with strongly correlated features to assess DMs' rule-learning abilities. Extensive experiments show that while DMs can identify coarse-grained rules, they struggle with fine-grained ones. Our theoretical analysis demonstrates that DMs trained via denoising score matching (DSM) exhibit constant errors in learning hidden rules, as the DSM objective is not compatible with rule conformity. To mitigate this, we introduce a common technique - incorporating additional classifier guidance during sampling, which achieves (limited) improvements. Our analysis reveals that the subtle signals of fine-grained rules are challenging for the classifier to capture, providing insights for future exploration.

Deep Learning

Junwei Su, shan Wu

Graph diffusion generative models (GDGMs) have emerged as powerful tools for generating high-quality graphs. However, their broader adoption faces challenges in \emph{scalability and size generalization}. GDGMs struggle to scale to large graphs due to their high memory requirements, as they typically operate in the full graph space, requiring the entire graph to be stored in memory during training and inference. This constraint limits their feasibility for large-scale real-world graphs. GDGMs also exhibit poor size generalization, with limited ability to generate graphs of sizes different from those in the training data, restricting their adaptability across diverse applications. To address these challenges, we propose the stochastic block graph diffusion (SBGD) model, which refines graph representations into a block graph space. This space incorporates structural priors based on real-world graph patterns, significantly reducing memory complexity and enabling scalability to large graphs. The block representation also improves size generalization by capturing fundamental graph structures. Empirical results show that SBGD achieves significant memory improvements (up to 6$\times$) while maintaining comparable or even superior graph generation performance relative to state-of-the-art methods. Furthermore, experiments demonstrate that SBGD better generalizes to unseen graph sizes. The significance of SBGD extends beyond being a scalable and effective GDGM; \emph{it also exemplifies the principle of modularization in generative modelling, offering a new avenue for exploring generative models by decomposing complex tasks into more manageable components.}

Applications · Health / Medicine

Sophia Tang, Yinuo Zhang, Pranam Chatterjee, PhD

We present **PepTune**, a multi-objective discrete diffusion model for simultaneous generation and optimization of therapeutic peptide SMILES. Built on the Masked Discrete Language Model (MDLM) framework, PepTune ensures valid peptide structures with a novel bond-dependent masking schedule and invalid loss function. To guide the diffusion process, we introduce **Monte Carlo Tree Guidance (MCTG)**, an inference-time multi-objective guidance algorithm that balances exploration and exploitation to iteratively refine Pareto-optimal sequences. MCTG integrates classifier-based rewards with search-tree expansion, overcoming gradient estimation challenges and data sparsity. Using PepTune, we generate diverse, chemically-modified peptides simultaneously optimized for multiple therapeutic properties, including target binding affinity, membrane permeability, solubility, hemolysis, and non-fouling for various disease-relevant targets. In total, our results demonstrate that MCTG for masked discrete diffusion is a powerful and modular approach for multi-objective sequence design in discrete state spaces.

Applications · Health / Medicine

Jiarui Lu, Xiaoyin Chen, Stephen Lu, Aurelie Lozano, Vijil Chenthamarakshan, Payel Das, Jian Tang

Protein dynamics play a crucial role in protein biological functions and properties, and their traditional study typically relies on time-consuming molecular dynamics (MD) simulations conducted in silico. Recent advances in generative modeling, particularly denoising diffusion models, have enabled efficient accurate protein structure prediction and conformation sampling by learning distributions over crystallographic structures. However, effectively integrating physical supervision into these data-driven approaches remains challenging, as standard energy-based objectives often lead to intractable optimization. In this paper, we introduce Energy-based Alignment (EBA), a method that aligns generative models with feedback from physical models, efficiently calibrating them to appropriately balance conformational states based on their energy differences. Experimental results on the MD ensemble benchmark demonstrate that EBA achieves state-of-the-art performance in generating high-quality protein ensembles. By improving the physical plausibility of generated structures, our approach enhances model predictions and holds promise for applications in structural biology and drug discovery.

Deep Learning · Generative Models and Autoencoders

Thibaut Issenhuth, Sangchul Lee, Ludovic Dos Santos, Jean-Yves Franceschi, Chansoo Kim, alain rakotomamonjy

Consistency models imitate the multi-step sampling of score-based diffusion in a single forward pass of a neural network.They can be learned in two ways: consistency distillation and consistency training. The former relies on the true velocity field of the corresponding differential equation, approximated by a pre-trained neural network.In contrast, the latter uses a single-sample Monte Carlo estimate of this velocity field.The related estimation error induces a discrepancy between consistency distillation and training that, we show, still holds in the continuous-time limit.To alleviate this issue, we propose a novel flow that transports noisy data towards their corresponding outputs derived from a consistency model.We prove that this flow reduces the previously identified discrepancy and the noise-data transport cost.Consequently, our method not only accelerates consistency training convergence but also enhances its overall performance. The code is available at https://github.com/thibautissenhuth/consistency_GC.

Deep Learning · Generative Models and Autoencoders

Zhuofan Zong, Dongzhi Jiang, Bingqi Ma, Guanglu Song, Hao Shao, Dazhong Shen, Yu Liu, Hongsheng Li

Significant achievements in personalization of diffusion models have been witnessed. Conventional tuning-free methods mostly encode multiple reference images by averaging or concatenating their image embeddings as the injection condition, but such an image-independent operation cannot perform interaction among images to capture consistent visual elements within multiple references. Although tuning-based approaches can effectively extract consistent elements within multiple images through the training process, it necessitates test-time finetuning for each distinct image group. This paper introduces EasyRef, a plug-and-play adaption method that empowers diffusion models to condition consistent visual elements (e.g., style and human facial identity, etc.) across multiple reference images under instruction controls. To effectively exploit consistent visual elements within multiple images, we leverage the multi-image comprehension and instruction-following capabilities of the multimodal large language model (MLLM), prompting it to capture consistent visual elements based on the instruction. Besides, injecting the MLLM's representations into the diffusion process through adapters can easily generalize to unseen domains. To mitigate computational costs and enhance fine-grained detail preservation, we introduce an efficient reference aggregation strategy and a progressive training scheme. Finally, we introduce MRBench, a new multi-reference image generation benchmark. Experimental results demonstrate EasyRef surpasses both tuning-free and tuning-based methods, achieving superior aesthetic quality and robust zero-shot generalization across diverse domains.

Probabilistic Methods

Yazid Janati, Badr MOUFAD, Mehdi Qassime, Alain Oliviero Durmus, Eric Moulines, Jimmy Olsson

Denoising diffusion models have driven significant progress in the field of Bayesian inverse problems. Recent approaches use pre-trained diffusion models as priors to solve a wide range of such problems, only leveraging inference-time compute and thereby eliminating the need to retrain task-specific models on the same dataset. To approximate the posterior of a Bayesian inverse problem, a diffusion model samples from a sequence of intermediate posterior distributions, each with an intractable likelihood function. This work proposes a novel mixture approximation of these intermediate distributions. Since direct gradient-based sampling of these mixtures is infeasible due to intractable terms, we propose a practical method based on Gibbs sampling. We validate our approach through extensive experiments on image inverse problems, utilizing both pixel- and latent-space diffusion priors, as well as on source separation with an audio diffusion model. The code is available at \url{https://www.github.com/badr-moufad/mgdm}.

Deep Learning · Large Language Models

Vaishnavh Nagarajan, Chen Wu, Charles Ding, Aditi Raghunathan

We design a suite of minimal algorithmic tasks that are a loose abstraction of _open-ended_ real-world tasks. This allows us to cleanly and controllably quantify the creative limits of the present-day language model.Much like real-world tasks that require a creative, far-sighted leap of thought, our tasks require an implicit, open-ended _stochastic_ planning step that either (a) discovers new connections in an abstract knowledge graph (like in wordplay, drawing analogies, or research) or (b) constructs new patterns (like in designing math problems or new proteins). In these tasks, we empirically and conceptually argue how next-token learning is myopic and memorizes excessively; multi-token approaches, namely teacherless training and diffusion models, comparatively excel in producing diverse and original output. Secondly, to elicit randomness without hurting coherence, we find that injecting noise at the input layer (dubbed _seed-conditioning_) works surprisingly as well as (and in some conditions, better than) temperature sampling from the output layer. Thus, our work offers a principled, minimal test-bed for analyzing open-ended creative skills, and offers new arguments for going beyond next-token learning and temperature sampling. We make part of the code available under https://github.com/chenwu98/algorithmic-creativity

Deep Learning · Generative Models and Autoencoders

Matthew Niedoba, Berend Zwartsenberg, Kevin Murphy, Frank Wood

We propose a simple, training-free mechanism which explains the generalization behaviour of diffusion models. By comparing pre-trained diffusion models to their theoretically optimal empirical counterparts, we identify a shared local inductive bias across a variety of network architectures. From this observation, we hypothesize that network denoisers generalize through localized denoising operations, as these operations approximate the training objective well over much of the training distribution. To validate our hypothesis, we introduce novel denoising algorithms which aggregate local empirical denoisers to replicate network behaviour. Comparing these algorithms to network denoisers across forward and reverse diffusion processes, our approach exhibits consistent visual similarity to neural network outputs, with lower mean squared error than previously proposed methods.

Applications · Everything Else

Boyu Zhang, Aocheng Shen, Bing Liu, Qiankun Zhang, Bin Yuan, Wang, Shenghao Liu, Xianjun Deng

We explore the potential of \emph{AI-enhanced combinatorial optimization theory}, taking online bipartite matching (OBM) as a case study.In the theoretical study of OBM, the \emph{hardness} corresponds to a performance \emph{upper bound} of a specific online algorithm or any possible online algorithms.Typically, these upper bounds derive from challenging instances meticulously designed by theoretical computer scientists.Zhang et al. (ICML 2024) recently provide an example demonstrating how reinforcement learning techniques enhance the hardness result of a specific OBM model.Their attempt is inspiring but preliminary.It is unclear whether their methods can be applied to other OBM problems with similar breakthroughs.This paper takes a further step by introducing DiMa, a unified and novel framework that aims at understanding the hardness of OBM problems based on denoising diffusion probabilistic models (DDPMs).DiMa models the process of generating hard instances as denoising steps, and optimizes them by a novel reinforcement learning algorithm, named \emph{shortcut policy gradient} (SPG).We first examine DiMa on the classic OBM problem by reproducing its known hardest input instance in literature.Further, we apply DiMa to two well-known variants of OBM, for which the exact hardness remains an open problem, and we successfully improve their theoretical state-of-the-art upper bounds.

Applications · Computer Vision

Kaifeng Gao, Jiaxin Shi, Hanwang Zhang, Chunping Wang, Jun Xiao, Long Chen

With the advance of diffusion models, today's video generation has achieved impressive quality. To extend the generation length and facilitate real-world applications, a majority of video diffusion models (VDMs) generate videos in an autoregressive manner, i.e., generating subsequent clips conditioned on the last frame(s) of the previous clip. However, existing autoregressive VDMs are highly inefficient and redundant: The model must re-compute all the conditional frames that are overlapped between adjacent clips. This issue is exacerbated when the conditional frames are extended autoregressively to provide the model with long-term context. In such cases, the computational demands increase significantly (i.e., with a quadratic complexity w.r.t. the autoregression step). In this paper, we propose **Ca2-VDM**, an efficient autoregressive VDM with **Ca**usal generation and **Ca**che sharing. For **causal generation**, it introduces unidirectional feature computation, which ensures that the cache of conditional frames can be precomputed in previous autoregression steps and reused in every subsequent step, eliminating redundant computations. For **cache sharing**, it shares the cache across all denoising steps to avoid the huge cache storage cost. Extensive experiments demonstrated that our Ca2-VDM achieves state-of-the-art quantitative and qualitative video generation results and significantly improves the generation speed. Code is available: https://github.com/Dawn-LX/CausalCache-VDM

Deep Learning · Generative Models and Autoencoders

Ting Jiang, Yixiao Wang, Hancheng Ye, Zishan Shao, Jingwei Sun, Jingyang Zhang, Zekai Chen, Jianyi Zhang, Yiran Chen, Hai Li

Diffusion models have achieved remarkable success in generative tasks but suffer from high computational costs due to their iterative sampling process and quadratic‐attention costs. Existing training-free acceleration strategies that reduce per-step computation cost, while effectively reducing sampling time, demonstrate low faithfulness compared to the original baseline. We hypothesize that this fidelity gap arises because (a) different prompts correspond to varying denoising trajectory, and (b) such methods do not consider the underlying ODE formulation and its numerical solution. In this paper, we propose **Stability-guided Adaptive Diffusion Acceleration (SADA)**, a novel paradigm that unifies step-wise and token-wise sparsity decisions via a single stability criterion to accelerate sampling of ODE-based generative models (Diffusion and Flow-matching). For (a), SADA adaptively allocates sparsity based on the sampling trajectory. For (b), SADA introduces principled approximation schemes that leverage the precise gradient information from the numerical ODE solver.Comprehensive evaluations on SD‐2, SDXL, and Flux using both EDM and DPM++ solvers reveal consistent $\ge 1.8\times$ speedups with minimal fidelity degradation (LPIPS $\leq 0.10$ and FID $\leq 4.5$) compared to unmodified baselines, significantly outperforming prior methods.Moreover, SADA adapts seamlessly to other pipelines and modalities: It accelerates ControlNet without any modifications and speeds up MusicLDM by \(1.8\times\) with \(\sim 0.01\) spectrogram LPIPS.Our code is available at: [https://github.com/Ting-Justin-Jiang/sada-icml](https://github.com/Ting-Justin-Jiang/sada-icml).