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Deep Learning · Generative Models and Autoencoders

Andrew Millard, Fredrik Lindsten, Zheng Zhao

We introduce a guided stochastic sampling method that augments sampling from diffusion models with physics-based guidance derived from partial differential equation (PDE) residuals and observational constraints, ensuring generated samples remain physically admissible. We embed this sampling procedure within a new Sequential Monte Carlo (SMC) framework, yielding a scalable generative PDE solver. Across multiple benchmark PDE systems as well as multiphysics and interacting PDE systems, our method produces solution fields with lower numerical error than existing state-of-the-art generative methods.

Deep Learning · Generative Models and Autoencoders

Jiacong Hu, Jinxun Wu, Shengxuming Zhang, Shunyu Liu, Haofei Zhang, Mingli Song, Zunlei Feng

Deep models are vulnerable to performance degradation caused by various factors, such as imbalanced samples, inaccurate labels, and backdoor attacks. However, existing optimization methods that address these issues are typically designed in a scenario- or architecture-specific manner, and each optimization often requires costly training. To this end, inspired by image denoising, we propose parameter purification as a new paradigm for model performance optimization. Parameter purification attributes performance degradation to the contamination of model parameters and aims to recover clean parameters from corrupted ones in a manner analogous to image denoising. To purify parameters with massive scale and complex structure, we further introduce a novel parameter manifold purification method. In this framework, high-dimensional and complex parameters are first viewed as manifolds embedded in a high-dimensional space, and are then partitioned into nested local parameter-cluster manifolds via a proposed parameter clustering strategy. Meanwhile, to remove parameter redundancy while preserving global parameter information, we propose an implicit manifold auto-encoder along with a parameter-cluster discrepancy loss to learn low-dimensional representations of parameter-cluster manifolds. Finally, an implicit conditional diffusion model is applied to denoise the low-dimensional parameter manifolds, progressively restoring clean parameters. Extensive experiments under three representative scenarios that cause model performance degradation demonstrate that parameter manifold purification can accurately and completely purify corrupted parameters of unseen models, analogous to denoising unseen images, and rapidly improve model performance.

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.

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

Yuxin Jiang, Yuchao Gu, Ivor Tsang, Mike Zheng Shou

Scaling action-controllable world models is limited by the scarcity of action labels. While latent action learning promises to extract control interfaces from unlabeled video, learned latents often fail to transfer across contexts: they entangle scene-specific cues and lack a shared coordinate system. This occurs because standard objectives operate only *within* each clip, providing no mechanism to align action semantics across contexts. Our key insight is that although actions are unobserved, their *semantic effects* are observable and can serve as a shared reference. We introduce **Seq$\Delta$-REPA**, a sequence-level control-effect alignment objective that anchors integrated latent action to temporal feature differences from a frozen, self-supervised video encoder. Building on this, we present **Olaf-World**, a pipeline that pretrains action-conditioned video world models from large-scale passive video. Extensive experiments demonstrate that our method learns a more structured latent action space, leading to stronger zero-shot action transfer and more data-efficient adaptation to new control interfaces than state-of-the-art baselines.

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.

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.

Deep Learning · Other Representation Learning

Hongfei Du, Jiacheng Shi, Sidi Lu, Gang Zhou, Ashley Gao

Integrating large language models (LLMs) into text-to-speech (TTS) systems has improved speech expressiveness, yet controllable emotional expression remains challenging. Existing approaches primarily rely on external conditioning or global activation steering, offering limited insight into how emotional variation is represented internally and restricting fine-grained control. In this work, we analyze emotion-related variation in the speech semantic hidden states of LLM-based TTS models. To this end, we leverage sparse autoencoders (SAEs) to map these representations to sparse latent features and examine their emotion-related activation patterns. Our evaluations indicate that emotional variation is distributed across multiple sparse latent features, revealing a more interpretable internal representation. Building on this observation, we introduce a feature-level intervention framework that enables targeted and bidirectional emotion induction and suppression without modifying backbone parameters. We further show that distinct latent features correlate with specific acoustic attributes (e.g., pitch), suggesting that emotional expression arises from coordinated latent contributions rather than a single global shift.

Deep Learning · Generative Models and Autoencoders

Zizhao Wang, Chang Shi, Jiaheng Hu, Kevin Rohling, Roberto Martín-Martín, Amy Zhang, Peter Stone

Learning latent actions from action-free video has emerged as a powerful paradigm for scaling up controllable world model learning. Latent actions provide a natural interface for users to iteratively generate and manipulate videos. However, most existing approaches rely on monolithic inverse and forward dynamics models that learn a single latent action to control the entire scene, and therefore struggle in complex environments where multiple entities act simultaneously. This paper introduces Factored Latent Action Model (FLAM), a factored dynamics framework that decomposes the scene into independent factors, each inferring its own latent action and predicting its own next-step factor value. This factorized structure enables more accurate modeling of complex multi-entity dynamics and improves video generation quality in action-free video settings compared to monolithic models. Based on experiments on both simulation and real-world multi-entity datasets, we find that FLAM outperforms prior work in prediction accuracy and representation quality, and facilitates downstream policy learning, demonstrating the benefits of factorized latent action models.

Deep Learning · Generative Models and Autoencoders

Dahee Kwon, Haeun Lee, Jaesik Choi

Recent text-to-image models built on large-scale Transformer backbones and flow-based objectives deliver strong text–image alignment and high visual quality, yet often produce overly similar samples under a fixed prompt. Existing diversity-enhancement methods can increase sample-to-sample variation, but typically rely on extra sampling, auxiliary optimization, or careful tuning—incurring non-trivial runtime and memory overhead. We examine intermediate Transformer features and observe that the lowest-frequency (DC) component rapidly homogenizes across seeds early in generation, infivsyinh an early trajectory lock-in that limits downstream variation. Building on this, we propose DC Attenuation for diVersity Enhancement \textbf{(DAVE)}, a training-free representation-level intervention that selectively attenuates this component in the early regime. DAVE preserves the sampling pipeline and incurs negligible overhead, improving prompt-consistent diversity without sacrificing image quality.

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.

Social Aspects · Accountability, Transparency, and Interpretability

Elias Shaheen, Avi Mendelson

The general-purpose nature of Large Language Models (LLMs) presents a significant challenge for domain-specific applications, often leading to out-of-domain (OOD) interactions that undermine the provider's intent. Existing methods for detecting such scenarios treat the LLM as an uninterpretable black box and overlook the internal processing of inputs. In this work we show that layer transitions provide a promising avenue for extracting domain-specific signature. Specifically, we present several lightweight ways of learning on internal dynamics encoded using a sparse autoencoder (SAE) that exhibit great capability in distinguishing OOD texts. Building on top of SAEs representation transitions enables us to better interpret the LLM internal evolution of input processing and shed light on its decisions. We provide a comprehensive analysis of the method and benchmark it with the gemma-2 2B and 9B models. Our results emphasize the efficacy of the internal process in capturing fine-grained input-related details.

Optimization · Stochastic

Alessandro Manenti, Cesare Alippi

Latent categorical variables are frequently found in deep learning architectures. They can model actions in discrete reinforcement-learning environments, represent categories in latent-variable models, or express relations in graph neural networks. Despite their widespread use, their discrete nature poses significant challenges to gradient-descent learning algorithms. While a substantial body of work has offered improved gradient estimation techniques, we take a complementary approach. Specifically, we: 1) revisit the ubiquitous *softmax* function and demonstrate its limitations from an information-geometric perspective; 2) replace the *softmax* with the *catnat* function, a function composed by a sequence of hierarchical binary splits; we prove that this choice offers significant advantages to gradient descent due to the resulting diagonal Fisher Information Matrix. A rich set of experiments - including graph structure learning, variational autoencoders, and reinforcement learning - empirically show that the proposed function improves the learning efficiency and yields models characterized by consistently higher test performance. *Catnat* is simple to implement and seamlessly integrates into existing codebases. Moreover, it remains compatible with standard training stabilization techniques and, as such, offers a better alternative to the *softmax* function.

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

Feiyang Fu, Hehe Fan

Discrete flow matching (DFM) provides a principled framework for generative modeling on discrete state spaces via continuous-time Markov chain dynamics. In practice, sampling for DFM commonly employs discretizations such as $\tau$-leaping, yet efficient sampling methods under a limited number of function evaluations (NFE) remain less studied. To address this gap, we propose the Time-Reparameterized Cumulative Intensity Extrapolation (TR-CIE) sampler, which aims to improve sampling quality when function evaluations are restricted. TR-CIE consists of two components. First, a schedule-based time reparameterization rescales the time grid according to the noise schedule. Under standard factorized DFM rate parameterizations, this transformation of variables absorbs the schedule-dependent growth term and mitigates stiffness near the terminal sampling stage. Second, we introduce a cumulative-intensity extrapolation updating rule. By reusing cached model outputs from the previous step as a history term, this improves the approximation of stepwise cumulative intensities on the resulting non-uniform time grid. We provide a theoretical analysis that bounds the local approximation error of cumulative intensities and establishes convergence results. The resulting sampler requires one NFE per step and introduces no additional model evaluations compared to the standard $\tau$-leaping sampler. Extensive experiments on synthetic tasks, text generation, and text-to-image benchmarks demonstrate that our method improves sampling quality under limited NFE.