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Deep Learning · Generative Models and Autoencoders

Gyeonghoon Ko, Juho Lee

Riemannian diffusion models generalize score-based generative modeling to manifold-supported data via stochastic diffusion equations on the manifold. However, training requires sampling from and differentiating the manifold heat kernel, which is rarely available in closed form beyond a few highly symmetric manifolds. We propose a general approach that approximates the heat kernel by directly solving the manifold heat equation with a physics-informed neural network (PINN). Given an explicit manifold specification, we choose a coordinate system, derive the corresponding heat (Fokker--Planck) equation and a short-time asymptotic approximation, and then train a PINN to learn the log heat kernel. The resulting surrogate enables both forward noising (heat-kernel sampling) and conditional-score evaluation for denoising score matching. We demonstrate the method on diverse manifolds including $S^2$, $SO(3)$, $\mathrm{SPD}(n)$, and permutation-quotiented point clouds.

Deep Learning · Generative Models and Autoencoders

Daan Roos, Oscar Davis, Floor Eijkelboom, Michael Bronstein, Max Welling, Ismail Ceylan, Luca Ambrogioni, Jan-Willem van de Meent

We introduce Categorical Flow Maps, a flow-matching method for accelerated few-step generation of categorical data via self-distillation. Building on recent variational formulations of flow matching and the broader trend towards accelerated inference in diffusion and flow-based models, we define a flow map towards the simplex that transports probability mass toward a predicted endpoint, yielding a parametrisation that naturally constrains model predictions. Since our trajectories are continuous rather than discrete, Categorical Flow Maps can be trained with existing distillation techniques, as well as a new objective based on endpoint consistency. This continuous formulation also automatically unlocks test-time inference: we can directly reuse existing guidance and reweighting techniques in the categorical setting to steer sampling toward downstream objectives. Empirically, we achieve state-of-the-art few-step results on images, molecular graphs, and text, with strong performance even in single-step generation.

Deep Learning · Generative Models and Autoencoders

Sol Park, Soobin Um

Minority sampling aims to generate low-density instances on a data manifold and is of central importance in applications such as medical diagnosis, anomaly detection, and creative AI. Existing approaches, however, define minority samples relative to generative priors learned from training data, confining rarity to model-specific notions that may poorly reflect real-world semantics. In this work, we propose a world-centric perspective on minority sampling, which defines rarity with respect to real-world priors rather than generator-induced densities. To this end, we introduce *JEPA guidance*, a diffusion sampling framework guided by a Joint-Embedding Predictive Architecture (JEPA)—a class of world models that encode broad, semantically rich representations. JEPA guidance steers diffusion trajectories toward low-density regions under the implicit density induced by the JEPA, thereby aligning generated minorities with real-world semantic rarity. To make JEPA guidance computationally practical, we develop principled approximation strategies accompanied by theoretical error bounds, significantly reducing the overhead of guidance computation. Extensive experiments across unconditional, class-conditional, and text-to-image generation demonstrate that JEPA guidance consistently improves the fidelity and semantic validity of minority samples, outperforming generator-centric baselines in capturing real-world notions of rarity.

General Machine Learning · Unsupervised and Semi-supervised Learning

Senyu Hou, Gaoxia Jiang, Xinyi Zheng, Yaqing Guo, Shuna Liang, Wenjian Wang

Label noise is pervasive in real-world datasets and significantly compromises model generalization, fueling extensive research into Learning with Noisy Labels (LNL). Most LNL methods focus on robust discriminative learning, while recent generative classifiers such as label diffusion models (LDMs) show superior robustness by modeling class posteriors. However, current LDMs predominantly rely on standard $\epsilon$-prediction, where Gaussian pnoise lacks explicit class semantics, limiting both optimization and inference under label noise environments. To address this issue, we propose just y-prediction (JYP), a novel training paradigm that enables LDMs to directly characterize the label manifold and leverage explicit class-semantic guidance. Theoretically, we prove that JYP converges to an optimal solution equivalent to that of $\epsilon$-prediction within the label diffusion framework, while facilitating accelerated convergence and enabling one-step inference. Leveraging JYP as a foundation, we further incorporate historical cumulative inconsistency to adaptively tailor optimization strategies for clean, noisy, and hard samples. Extensive experiments demonstrate that our method consistently outperforms competitors across diverse synthetic noisy datasets and achieves state-of-the-art performance on multiple real-world benchmarks.

Deep Learning · Generative Models and Autoencoders

Jiaoyang Ruan, Xin Gao, Yinda Chen, Hengyu Zeng, Liang Du, Guanghao Li, Jie Fu, Jian Pu

While Diffusion Large Language Models (dLLMs) offer structural advantages for global planning, efficiently verifying that they arrive at correct answers via valid reasoning traces remains a critical challenge. In this work, we propose a geometric perspective: Reasoning on the Manifold. We hypothesize that valid generation trajectories reside as stable attractors on the high-density manifold of the learned distribution, whereas invalid paths exhibit off-manifold drift. To operationalize this, we introduce Bidirectional Manifold Consistency (BMC), a training-free, unsupervised metric that quantifies the stability of the generated sequence through a forward-masking and backward-reconstruction cycle. Empirically, we demonstrate BMC's versatility across the full reasoning lifecycle: (1) in Diagnosis, it serves as a robust discriminator of solution validity without ground truth answer; (2) in Inference, it enables rejection resampling to effectively concentrate computational resources on complex reasoning tasks; and (3) in Alignment, it functions as a dense geometric reward that transforms sparse outcome supervision into fine-grained guidance, empowering models to self-evolve beyond standard baselines. Our results establish intrinsic geometric stability as a robust indicator of correctness for dLLMs.

Deep Learning · Generative Models and Autoencoders

Haoyang Chen, Jing Zhang, Hebaixu Wang, Shiqin Wang, Pohsun Huang, Jiayuan Li, Haonan Guo, Di Wang, Zheng Wang, Bo Du

Multi-modal remote sensing imagery provides complementary observations of the same geographic scene, yet such observations are frequently incomplete in practice. Existing cross-modal translation methods treat each modality pair as an independent task, resulting in quadratic complexity and limited generalization to unseen modality combinations. We formulate Any-to-Any translation as inference over a shared latent representation of the scene, where different modalities correspond to partial observations of the same underlying semantics. Based on this formulation, we propose Any2Any, a unified latent diffusion framework that projects heterogeneous inputs into a geometrically aligned latent space. Such structure performs anchored latent regression with a shared backbone, decoupling modality-specific representation learning from semantic mapping. Moreover, lightweight target-specific residual adapters are used to correct systematic latent mismatches without increasing inference complexity. To support learning under sparse but connected supervision, we introduce RST-1M, the first million-scale remote sensing dataset with paired observations across five sensing modalities, providing supervision anchors for any-to-any translation. Experiments across 14 translation tasks show that Any2Any consistently outperforms pairwise translation methods and exhibits strong zero-shot generalization to unseen modality pairs.

Deep Learning · Generative Models and Autoencoders

Kijung Jeon, Michael Muehlebach, Molei Tao

Generative modeling within constrained sets is essential for scientific and engineering applications involving physical, geometric, or safety requirements (e.g., molecular generation, robotics). We present a unified framework for constrained diffusion models on generic nonconvex feasible sets $\Sigma$ that simultaneously enforces equality and inequality constraints throughout the diffusion process. Our framework incorporates both overdamped and underdamped dynamics for forward and backward sampling. A key algorithmic innovation is a computationally efficient landing mechanism that replaces costly and often ill-defined projections onto $\Sigma$, ensuring feasibility without iterative Newton solves or projection failures. By leveraging underdamped dynamics, we accelerate mixing toward the prior distribution, effectively alleviating the high simulation costs typically associated with constrained diffusion. Empirically, this approach reduces function evaluations and memory usage during both training and inference while preserving sample quality. On benchmarks featuring equality and mixed constraints, our method achieves comparable sample quality to state-of-the-art baselines while significantly reducing computational cost, providing a practical and scalable solution for diffusion on nonconvex feasible sets.

Deep Learning · Generative Models and Autoencoders

Jiangshan Wang, Zeqiang Lai, Jiarui Chen, Jiayi Guo, Hang Guo, Xiu Li, Xiangyu Yue, Chunchao Guo

Diffusion Transformers (DiT) have demonstrated remarkable generative capabilities but remain highly computationally expensive. Previous acceleration methods, such as pruning and distillation, typically rely on a fixed computational capacity, leading to insufficient acceleration and degraded generation quality. To address this limitation, we propose \textbf{Elastic Diffusion Transformer (E-DiT)}, an adaptive acceleration framework for DiT that effectively improves efficiency while maintaining generation quality. Specifically, we observe that the generative process of DiT exhibits substantial sparsity (i.e., some computations can be skipped with minimal impact on quality), and this sparsity varies significantly across samples. Motivated by this observation, E-DiT equips each DiT block with a lightweight router that dynamically identifies sample-dependent sparsity from the input latent. Each router adaptively determines whether the corresponding block can be skipped. If the block is not skipped, the router then predicts the optimal MLP width reduction ratio within the block. During inference, we further introduce a block-level feature caching mechanism that leverages router predictions to eliminate redundant computations in a training-free manner. Extensive experiments across 2D image (Qwen-Image and FLUX) and 3D asset (Hunyuan3D-3.0) demonstrate the effectiveness of E-DiT, achieving up to $\sim$2$\times$ speedup with negligible loss in generation quality.

Deep Learning · Generative Models and Autoencoders

Jaemoo Choi, Yuchen Zhu, Wei Guo, Petr Molodyk, Bo Yuan, Jinbin Bai, Yi Xin, Molei Tao, Yongxin Chen

Reinforcement learning has been widely applied to diffusion and flow models for visual tasks such as text-to-image generation. However, these tasks remain challenging because diffusion models have intractable likelihoods, which creates a barrier for directly applying popular policy-gradient type methods. Existing approaches primarily focus on crafting new objectives built on already heavily engineered LLM objectives, using ad hoc estimators for likelihood, without a thorough investigation into how such estimation affects overall algorithmic performance. In this work, we provide a systematic analysis of the RL design space by disentangling three factors: i) policy-gradient objectives, ii) likelihood estimators, and iii) rollout sampling schemes. We show that adopting an evidence lower bound (ELBO) based model likelihood estimator, computed only from the final generated sample, is the dominant factor enabling effective, efficient, and stable RL optimization, outweighing the impact of the specific policy-gradient loss functional. We validate our findings across multiple reward benchmarks using SD 3.5 Medium, and observe consistent trends across all tasks. Our method improves the GenEval score from $0.24$ to $0.95$ in $90$ GPU hours, which is $4.6\times$ more efficient than FlowGRPO and $2\times$ more efficient than the SOTA method DiffusionNFT without reward hacking.

Applications · Time Series

Han Zhang, Nenggan Zheng

Long-horizon motion prediction under external commands is challenged by latent decision uncertainty, where the internal states governing future behavior are unobservable and evolve stochastically over time. This issue is particularly pronounced in biological agents, whose motion trajectories reflect decision-making processes rooted in underlying cognitive states. To address these challenges, we propose CogSDE, a formulation of the controlled stochastic differential equation (SDE) for modeling instruction-driven latent decision dynamics. The drift term in the SDE incorporates a dual-channel control modulation mechanism, enabling external commands to modulate the latent state evolution. The diffusion term in the SDE adopts a state-dependent operator to model intrinsic uncertainty in latent decision dynamics. Furthermore, we establish a theoretical upper bound on the long-horizon prediction of CogSDE through dissipativity-based analysis. Experiments demonstrate that CogSDE consistently improves predictive accuracy in long-horizon motion generation. Importantly, predicted trajectories remain well aligned with control instructions over extended horizons, a property widely recognized as challenging in long-horizon motion prediction.

Deep Learning · Generative Models and Autoencoders

Nick Dodson, Xinyu Gao, Qingsong Wang, Yusu Wang, Zhengchao Wan

Diffusion models generate high-quality samples but can also memorize training data, raising serious privacy concerns. Understanding the mechanisms governing when memorization versus generalization occurs remains an active area of research. In particular, it is unclear where along the noise schedule memorization is induced, how data geometry influences it, and how phenomena at different noise scales interact. We introduce a geometric framework that partitions the noise schedule into three regimes based on the coverage properties of training data by Gaussian shells and the concentration behavior of the posterior, which we argue are two fundamental objects governing memorization and generalization in diffusion models. This perspective reveals that memorization risk is highly non-uniform across noise levels. We further identify a danger zone at medium noise levels where memorization is most pronounced. In contrast, both the small and large noise regimes resist memorization, but through fundamentally different mechanisms: small noise avoids memorization due to limited training coverage, while large noise exhibits low posterior concentration and admits a provably near linear Gaussian denoising behavior. For the medium noise regime, we identify geometric conditions through which we propose a geometry-informed targeted intervention that mitigates memorization.

Yihong Luo, Tianyang Hu, Weijian Luo, Jing Tang

While few-step generative models have enabled powerful image and video generation at significantly lower cost, generic reinforcement learning (RL) paradigms for few-step models remain an unsolved problem. Existing RL approaches for few-step diffusion models strongly rely on back-propagating through differentiable reward models, thereby excluding the majority of important real-world reward signals, e.g., non-differentiable rewards such as humans' binary likeness, object counts, etc. To properly incorporate non-differentiable rewards to improve few-step generative models, we introduce TDM-R1, a novel reinforcement learning paradigm built upon a leading few-step model, Trajectory Distribution Matching (TDM). TDM-R1 decouples the learning process into surrogate reward learning and generator learning. Furthermore, we developed practical methods to obtain per-step reward signals along the deterministic generation trajectory of TDM, resulting in a unified RL post-training method that significantly improves few-step models' ability with generic rewards. We conduct extensive experiments ranging from text-rendering, visual quality, and preference alignment. All results demonstrate that TDM-R1 is a powerful reinforcement learning paradigm for few-step text-to-image models, achieving state-of-the-art reinforcement learning performances on both in-domain and out-of-domain metrics.

Deep Learning · Generative Models and Autoencoders

Dongyeop Woo, Marta Skreta, Seonghyun Park, Kirill Neklyudov, Sungsoo Ahn

Diffusion and flow models have become the dominant paradigm for generative modeling on Riemannian manifolds, with successful applications in protein backbone generation and DNA sequence design. However, these methods require tens to hundreds of neural network evaluations at inference time, which can become a computational bottleneck in large-scale scientific sampling workflows. We introduce Riemannian MeanFlow (RMF), a framework for learning flow maps directly on manifolds, enabling high-quality generations with as few as one forward pass. We derive three equivalent characterizations of the manifold average velocity (Eulerian, Lagrangian, and semigroup identities), and analyze parameterizations and stabilization techniques to improve training on high-dimensional manifolds. In promoter DNA design and protein backbone generation settings, RMF achieves comparable sample quality to prior methods while requiring up to 10$\times$ fewer function evaluations. Finally, we show that few-step flow maps enable efficient reward-guided design through reward look-ahead, where terminal states can be predicted from intermediate steps at minimal additional cost.

Applications · Health / Medicine

Zelin Zang, WenZhe Li, Yongjie Xu, Chang Yu, Changxi Chi, Jingbo Zhou, Zhen Lei, Stan Z Li

In single-cell research, tracing and analyzing high-throughput single-cell differentiation trajectories is crucial for understanding biological processes. Key to this is the robust modeling of hierarchical structures that govern cellular development. Traditional methods face limitations in computational cost, performance, and stability. VAE-based approaches have made strides but still require branch-specific network modules, limiting their scalability and stability, while often suffering from posterior collapse. To overcome these challenges, we introduce HDTree, a generative modeling framework designed for robust lineage inference. HDTree captures tree relationships within a hierarchical latent space using a unified hierarchical codebook and employs a quantized diffusion process to model continuous cell state transitions. By aligning the generative process with the Waddington landscape, this method not only improves stability and scalability but also enhances the biological plausibility of inferred lineages. HDTree's effectiveness is demonstrated through comparisons on both general-purpose and single-cell datasets, where it outperforms existing methods in lineage inference accuracy, reconstruction quality, and hierarchical consistency. These contributions enable accurate and efficient modeling of cellular differentiation paths, offering reliable insights for biological discovery.

Deep Learning · Large Language Models

Xiang Fang, Wanlong Fang

In the era of Large Video-Language Models (LVLMs), the computational necessity of sparse frame sampling creates a fundamental ``temporal gap'', rendering models blind to critical causal transitions. Existing solutions relying on generative hallucination (e.g., latent diffusion) or autoregressive extrapolation often fail to maintain semantic consistency over long horizons, suffering from object vanishing and energetic instability. We propose a paradigm shift from probabilistic generation to variational mechanics with the \textbf{Semantic Least Action Principle (SLAP)}. Drawing a rigorous isomorphism between classical mechanics and semantic dynamics, we model the latent video trajectory as a path on a Riemannian manifold governed by a Semantic Lagrangian. By formulating the interpolation task as a Boundary Value Problem (BVP) solved via the discrete Euler-Lagrange equations, SLAP naturally enforces object persistence without pixel-level rendering. Extensive experiments on multiple challenging datasets show the effectiveness of our proposed SLAP.

Social Aspects · Privacy

Antoni Kowalczuk, Dominik Hintersdorf, Lukas Struppek, Kristian Kersting, Adam Dziedzic, Franziska Boenisch

Text-to-image diffusion models (DMs) have achieved remarkable success in image generation. However, concerns about data privacy and intellectual property remain due to their potential to inadvertently memorize and replicate training data. Recent mitigation efforts have focused on identifying and pruning weights responsible for triggering verbatim training data replication, based on the assumption that memorization can be localized. We challenge this assumption and demonstrate that, even after such pruning, small perturbations to the text embeddings of previously mitigated prompts can re-trigger data replication, revealing the fragility of such methods. Our further analysis then provides multiple indications that memorization is indeed *not* inherently local: (1) replication triggers for memorized images are distributed throughout text embedding space; (2) embeddings yielding the same replicated image produce divergent model activations; and (3) different pruning methods identify inconsistent sets of memorization-related weights for the same image. Finally, we show that bypassing the locality assumption enables more robust mitigation through adversarial fine-tuning. These findings provide new insights into the fundamental nature of memorization in text-to-image DMs and inform the future development of more reliable mitigation methods against DM memorization.

Probabilistic Methods · Variational Inference

Qilin Liao, Anamika Lochab, Ruqi Zhang

Vision-Language Models (VLMs) extend large language models with visual reasoning, but their multimodal design also introduces new, underexplored vulnerabilities. Existing multimodal red-teaming methods largely rely on brittle templates, focus on single-attack settings, and expose only a narrow subset of vulnerabilities. To address these limitations, we introduce VERA-V, a variational inference framework that recasts multimodal jailbreak discovery as learning a joint posterior distribution over paired text-image prompts. This probabilistic view captures complex cross-modal interactions, enabling stealthy, coordinated adversarial inputs that bypass model guardrails. We train a lightweight attacker to approximate the posterior, allowing efficient sampling of diverse jailbreaks and providing distributional insights into vulnerabilities. VERA-V further integrates three complementary strategies: (i) typography-based text prompts that embed harmful cues, (ii) diffusion-based image synthesis that introduces adversarial signals, and (iii) structured distractors to fragment VLM attention. Experiments on HarmBench and HADES benchmarks show that VERA-V consistently outperforms state-of-the-art baselines on both open-source and frontier VLMs, achieving up to 53.75\% higher attack success rate (ASR) over the best baseline on GPT-4o.

Probabilistic Methods · Monte Carlo and Sampling Methods

Fan Chen, Sinho Chewi, Constantinos Daskalakis, Alexander Rakhlin

We present algorithms for diffusion model sampling which obtain $\delta$-error in $\mathrm{polylog}(1/\delta)$ steps, given access to $\widetilde O(\delta)$-accurate score estimates in $L^2$. This is an exponential improvement over all previous results. Specifically, under minimal data assumptions, the complexity is $\widetilde O(d\mathrm{polylog}(1/\delta))$ where $d$ is the dimension of the data; under a non-uniform $L$-Lipschitz condition, the complexity is $\widetilde O(\sqrt{dL}\mathrm{polylog}(1/\delta))$; and if the data distribution has intrinsic dimension $d_\star$, then the complexity reduces to $\widetilde O(d_\star\mathrm{polylog}(1/\delta))$. Our approach also yields the first $\mathrm{polylog}(1/\delta)$ complexity sampler for general log-concave distributions using only gradient evaluations.

Deep Learning · Generative Models and Autoencoders

Wenlan Chen, Lu Gao, Daoyuan Wang, Cheng Liang, Fei Guo

Incomplete multi-view clustering is challenging due to view missingness and the entanglement of shared semantics with view-specific factors in latent representations. Existing methods often rely on heuristic fusion or direct completion strategies, which suffer from error propagation and unreliable generation under missing views. In this paper, we propose an **I**nformation-guided **D**isentangled latent modeling framework with **C**onditional **D**iffusion for incomplete multi-view clustering (IDCD). Specifically, we first encode each view into a latent representation that is variationally decomposed into a view-wise semantic latent and a view-specific factor. Information-theoretic objectives are introduced to guide the disentanglement of view-wise latents, preserving essential multi-view information while reducing the dependency between semantic and view-specific factors and encouraging cross-view semantic consistency. Besides, we aggregate the semantic latents via a mixture of Wasserstein distributions to obtain a unified global representation, where we impose a Gaussian mixture prior to explicitly couple representation learning with clustering. Based on the learned disentangled latent space, a conditional diffusion model guided by both the global semantic latent and view-specific factors is employed to generate missing views in a consistent manner. Extensive experiments on benchmark datasets demonstrate superior clustering performance and robust missing-view generation compared to state-of-the-art methods.

Deep Learning · Generative Models and Autoencoders

Zihao Cheng, Binrui Wu, Yuesen Liao, Weizhong Zhang

Diffusion probabilistic models (DPMs)’ sampling process is often inefficient, requiring hundreds to thousands of iterative steps to accurately approximate the diffusion trajectory. This inefficiency limits their practical applicability. Although recent advances in sampling efficiency—such as numerical solvers for diffusion ordinary differential equations (ODEs)—have made progress, significant challenges remain: training-free numerical solvers suffer from the suboptimality of manually designed timestep selection rules and the inherent inconsistency between the forward diffusion process (typically involving thousands of steps) and the reverse denoising process (usually limited to tens of steps). Since timestep selection is inherently a discrete problem and cannot be optimized via gradients, we propose an innovative approach—reparameterizing the timestep scheduling through probabilistic masking, thereby enabling gradient-based optimization of sampling timesteps. To circumvent backpropagation, we employ policy gradient methods. Furthermore, to address the inconsistency between forward diffusion (training) and reverse denoising (inference), we extend this framework into a bilevel optimization paradigm: the inner loop performs additional lightweight training on the model at specific timesteps determined by the outer mask to align forward and reverse processes, while the outer loop optimizes the timestep distribution via probabilistic masking and policy gradient based on generation quality. Under mild assumptions, we theoretically analyze the convergence of the proposed algorithm. Extensive experiments across diverse datasets and samplers demonstrate that this framework effectively enhances sampling efficiency and generation quality while maintaining compatibility with various DPM architectures and advanced ODE solvers.