Improving Diffusion-based Inverse Algorithms under Few-Step Constraint via Learnable Linear Extrapolation

Diffusion models have demonstrated remarkable performance in modeling complex data priors, catalyzing their widespread adoption in solving various inverse problems. However, the inherently iterative nature of diffusion-based inverse algorithms often requires hundreds to thousands of steps, with performance degradation occurring under fewer steps which limits their practical applicability. While high-order diffusion ODE solvers have been extensively explored for efficient diffusion sampling without observations, their application to inverse problems remains underexplored due to the diverse forms of inverse algorithms and their need for repeated trajectory correction based on observations. To address this gap, we first introduce a canonical form that decomposes existing diffusion-based inverse algorithms into three modules to unify their analysis. Inspired by the linear subspace search strategy in the design of high-order diffusion ODE solvers, we propose the Learnable Linear Extrapolation (LLE) method, a lightweight approach that universally enhances the performance of any diffusion-based inverse algorithm that fits the proposed canonical form. Extensive experiments demonstrate consistent improvements of the proposed LLE method across multiple algorithms and tasks, indicating its potential for more efficient solutions and boosted performance of diffusion-based inverse algorithms with limited steps. Codes for reproducing our experiments are available at \href{https://github.com/weigerzan/LLE_inverse_problem}{https://github.com/weigerzan/LLE\_inverse\_problem}.

Minimax Optimality of the Probability Flow ODE for Diffusion Models

Score-based diffusion models have become a foundational paradigm for modern generative modeling, demonstrating exceptional capability in generating samples from complex high-dimensional distributions. Despite the dominant adoption of probability flow ODE-based samplers in practice due to their superior sampling efficiency and precision, rigorous statistical guarantees for these methods have remained elusive in the literature. This work develops the first end-to-end theoretical framework for deterministic ODE-based samplers that establishes near-minimax optimal guarantees under mild assumptions on target data distributions. Specifically, focusing on subgaussian distributions with $\beta$-H\"older smooth densities for $\beta\leq 2$, we propose a smooth regularized score estimator that simultaneously controls both the $L^2$ score error and the associated mean Jacobian error. Leveraging this estimator within a refined convergence analysis of the ODE-based sampling process, we demonstrate that the resulting sampler achieves the minimax rate in total variation distance, modulo logarithmic factors. Notably, our theory comprehensively accounts for all sources of error in the sampling process and does not require strong structural conditions such as density lower bounds or Lipschitz/smooth scores on target distributions, thereby covering a broad range of practical data distributions.

AR-Diffusion: Asynchronous Video Generation with Auto-Regressive Diffusion

The task of video generation requires synthesizing visually realistic and temporally coherent video frames. Existing methods primarily use asynchronous auto-regressive models or synchronous diffusion models to address this challenge. However, asynchronous auto-regressive models often suffer from inconsistencies between training and inference, leading to issues such as error accumulation, while synchronous diffusion models are limited by their reliance on rigid sequence length. To address these issues, we introduce Auto-Regressive Diffusion (AR-Diffusion), a novel model that combines the strengths of auto-regressive and diffusion models for flexible, asynchronous video generation. Specifically, our approach leverages diffusion to gradually corrupt video frames in both training and inference, reducing the discrepancy between these phases. Inspired by auto-regressive generation, we incorporate a non-decreasing constraint on the corruption timesteps of individual frames, ensuring that earlier frames remain clearer than subsequent ones. This setup, together with temporal causal attention, enables flexible generation of videos with varying lengths while preserving temporal coherence. In addition, we design two specialized timestep schedulers: the FoPP scheduler for balanced timestep sampling during training, and the AD scheduler for flexible timestep differences during inference, supporting both synchronous and asynchronous generation. Extensive experiments demonstrate the superiority of our proposed method, which achieves competitive and state-of-the-art results across four challenging benchmarks.

Resource-Efficient Affordance Grounding with Complementary Depth and Semantic Prompts

Affordance refers to the functional properties that an agent perceives and utilizes from its environment, and is key perceptual information required for robots to perform actions. This information is rich and multimodal in nature. Existing multimodal affordance methods face limitations in extracting useful information, mainly due to simple structural designs, basic fusion methods, and large model parameters, making it difficult to meet the performance requirements for practical deployment. To address these issues, this paper proposes the BiT-Align image-depth-text affordance mapping framework. The framework includes a Bypass Prompt Module (BPM) and a Text Feature Guidance (TFG) attention selection mechanism. BPM integrates the auxiliary modality depth image directly as a prompt to the primary modality RGB image, embedding it into the primary modality encoder without introducing additional encoders. This reduces the model's parameter count and effectively improves functional region localization accuracy. The TFG mechanism guides the selection and enhancement of attention heads in the image encoder using textual features, improving the understanding of affordance characteristics. Experimental results demonstrate that the proposed method achieves significant performance improvements on public AGD20K and HICO-IIF datasets. On the AGD20K dataset, compared with the current state-of-the-art method, we achieve a 6.0% improvement in the KLD metric, while reducing model parameters by 88.8%, demonstrating practical application values. The source code will be made publicly available at https://github.com/DAWDSE/BiT-Align.

Nonlinear Sparse Generalized Canonical Correlation Analysis for Multi-view High-dimensional Data

Motivation: Biomedical studies increasingly produce multi-view high-dimensional datasets (e.g., multi-omics) that demand integrative analysis. Existing canonical correlation analysis (CCA) and generalized CCA methods address at most two of the following three key aspects simultaneously: (i) nonlinear dependence, (ii) sparsity for variable selection, and (iii) generalization to more than two data views. There is a pressing need for CCA methods that integrate all three aspects to effectively analyze multi-view high-dimensional data. Results: We propose three nonlinear, sparse, generalized CCA methods, HSIC-SGCCA, SA-KGCCA, and TS-KGCCA, for variable selection in multi-view high-dimensional data. These methods extend existing SCCA-HSIC, SA-KCCA, and TS-KCCA from two-view to multi-view settings. While SA-KGCCA and TS-KGCCA yield multi-convex optimization problems solved via block coordinate descent, HSIC-SGCCA introduces a necessary unit-variance constraint previously ignored in SCCA-HSIC, resulting in a nonconvex, non-multiconvex problem. We efficiently address this challenge by integrating the block prox-linear method with the linearized alternating direction method of multipliers. Simulations and TCGA-BRCA data analysis demonstrate that HSIC-SGCCA outperforms competing methods in multi-view variable selection.

Minimax-Optimal Multi-Agent Robust Reinforcement Learning

Multi-agent robust reinforcement learning, also known as multi-player robust Markov games (RMGs), is a crucial framework for modeling competitive interactions under environmental uncertainties, with wide applications in multi-agent systems. However, existing results on sample complexity in RMGs suffer from at least one of three obstacles: restrictive range of uncertainty level or accuracy, the curse of multiple agents, and the barrier of long horizons, all of which cause existing results to significantly exceed the information-theoretic lower bound. To close this gap, we extend the Q-FTRL algorithm \citep{li2022minimax} to the RMGs in finite-horizon setting, assuming access to a generative model. We prove that the proposed algorithm achieves an $\varepsilon$-robust coarse correlated equilibrium (CCE) with a sample complexity (up to log factors) of $\widetilde{O}\left(H^3S\sum_{i=1}^mA_i\min\left\{H,1/R\right\}/\varepsilon^2\right)$, where $S$ denotes the number of states, $A_i$ is the number of actions of the $i$-th agent, $H$ is the finite horizon length, and $R$ is uncertainty level. We also show that this sample compelxity is minimax optimal by combining an information-theoretic lower bound. Additionally, in the special case of two-player zero-sum RMGs, the algorithm achieves an $\varepsilon$-robust Nash equilibrium (NE) with the same sample complexity.

Condense, Don't Just Prune: Enhancing Efficiency and Performance in MoE Layer Pruning

Mixture-of-Experts (MOE) has garnered significant attention for their ability to scale up neural networks while utilizing the same or even fewer active parameters. However, MoE does not relieve the massive memory requirements of networks, which limits their practicality in real-world applications, especially in the era of large language models (LLMs). While recent work explores the possibility of removing entire layers of MoE to reduce memory, the performance degradation is still notable. In this paper, we propose Condense-MoE (CD-MoE} that, instead of dropping the entire MoE layer, condenses the big, sparse MoE layer into a small but dense layer with only a few experts that are activated for all tokens. Our approach is specifically designed for fine-grained MoE with shared experts, where Feed-Forward Networks are split into many small experts, with certain experts isolated to serve as shared experts that are always activated. We demonstrate the effectiveness of our method across multiple MoE models such as DeepSeekMoE and QwenMoE on various benchmarks. Specifically, for the DeepSeekMoE-16B model, our approach maintains nearly 90% of the average accuracy while reducing memory usage by 30% and enhancing inference speed by 30%. Moreover, we show that with lightweight expert fine-tuning, the pruned model can achieve further improvements on specific tasks. Our code are available at https://github.com/duterscmy/CD-MoE/tree/main.

Principles of Visual Tokens for Efficient Video Understanding

Video understanding has made huge strides in recent years, relying largely on the power of the transformer architecture. As this architecture is notoriously expensive and video is highly redundant, research into improving efficiency has become particularly relevant. This has led to many creative solutions, including token merging and token selection. While most methods succeed in reducing the cost of the model and maintaining accuracy, an interesting pattern arises: most methods do not outperform the random sampling baseline. In this paper we take a closer look at this phenomenon and make several observations. First, we develop an oracle for the value of tokens which exposes a clear Pareto distribution where most tokens have remarkably low value, and just a few carry most of the perceptual information. Second, we analyze why this oracle is extremely hard to learn, as it does not consistently coincide with visual cues. Third, we observe that easy videos need fewer tokens to maintain accuracy. We build on these and further insights to propose a lightweight video model we call LITE that can select a small number of tokens effectively, outperforming state-of-the-art and existing baselines across datasets (Kinetics400 and Something-Something-V2) in the challenging trade-off of computation (GFLOPs) vs accuracy.

BAMITA: Bayesian Multiple Imputation for Tensor Arrays

Data increasingly take the form of a multi-way array, or tensor, in several biomedical domains. Such tensors are often incompletely observed. For example, we are motivated by longitudinal microbiome studies in which several timepoints are missing for several subjects. There is a growing literature on missing data imputation for tensors. However, existing methods give a point estimate for missing values without capturing uncertainty. We propose a multiple imputation approach for tensors in a flexible Bayesian framework, that yields realistic simulated values for missing entries and can propagate uncertainty through subsequent analyses. Our model uses efficient and widely applicable conjugate priors for a CANDECOMP/PARAFAC (CP) factorization, with a separable residual covariance structure. This approach is shown to perform well with respect to both imputation accuracy and uncertainty calibration, for scenarios in which either single entries or entire fibers of the tensor are missing. For two microbiome applications, it is shown to accurately capture uncertainty in the full microbiome profile at missing timepoints and used to infer trends in species diversity for the population. Documented R code to perform our multiple imputation approach is available at https://github.com/lockEF/MultiwayImputation .

Provable acceleration for diffusion models under minimal assumptions

While score-based diffusion models have achieved exceptional sampling quality, their sampling speeds are often limited by the high computational burden of score function evaluations. Despite the recent remarkable empirical advances in speeding up the score-based samplers, theoretical understanding of acceleration techniques remains largely limited. To bridge this gap, we propose a novel training-free acceleration scheme for stochastic samplers. Under minimal assumptions -- namely, $L^2$-accurate score estimates and a finite second-moment condition on the target distribution -- our accelerated sampler provably achieves $\varepsilon$-accuracy in total variation within $\widetilde{O}(d^{5/4}/\sqrt{\varepsilon})$ iterations, thereby significantly improving upon the $\widetilde{O}(d/\varepsilon)$ iteration complexity of standard score-based samplers. Notably, our convergence theory does not rely on restrictive assumptions on the target distribution or higher-order score estimation guarantees.