We present Articulated Kinematics Distillation (AKD), a framework for generating high-fidelity character animations by merging the strengths of skeleton-based animation and modern generative models. AKD uses a skeleton-based representation for rigged 3D assets, drastically reducing the Degrees of Freedom (DoFs) by focusing on joint-level control, which allows for efficient, consistent motion synthesis. Through Score Distillation Sampling (SDS) with pre-trained video diffusion models, AKD distills complex, articulated motions while maintaining structural integrity, overcoming challenges faced by 4D neural deformation fields in preserving shape consistency. This approach is naturally compatible with physics-based simulation, ensuring physically plausible interactions. Experiments show that AKD achieves superior 3D consistency and motion quality compared with existing works on text-to-4D generation.

Masked diffusion models (MDMs) have emerged as a popular research topic for generative modeling of discrete data, thanks to their superior performance over other discrete diffusion models, and are rivaling the auto-regressive models (ARMs) for language modeling tasks. The recent effort in simplifying the masked diffusion framework further leads to alignment with continuous-space diffusion models and more principled training and sampling recipes. In this paper, however, we reveal that both training and sampling of MDMs are theoretically free from the time variable, arguably the key signature of diffusion models, and are instead equivalent to masked models. The connection on the sampling aspect is drawn by our proposed first-hitting sampler (FHS). Specifically, we show that the FHS is theoretically equivalent to MDMs' original generation process while significantly alleviating the time-consuming categorical sampling and achieving a 20$\times$ speedup. In addition, our investigation raises doubts about whether MDMs can truly beat ARMs in text generation. We identify, for the first time, an underlying numerical issue, even with the commonly used 32-bit floating-point precision, which results in inaccurate categorical sampling. We show that it lowers the effective temperature both theoretically and empirically, and the resulting decrease in token diversity makes previous evaluations, which assess the generation quality solely through the incomplete generative perplexity metric, somewhat unfair.

While likelihood-based generative models, particularly diffusion and autoregressive models, have achieved remarkable fidelity in visual generation, the maximum likelihood estimation (MLE) objective, which minimizes the forward KL divergence, inherently suffers from a mode-covering tendency that limits the generation quality under limited model capacity. In this work, we propose Direct Discriminative Optimization (DDO) as a unified framework that integrates likelihood-based generative training and GAN-type discrimination to bypass this fundamental constraint by exploiting reverse KL and self-generated negative signals. Our key insight is to parameterize a discriminator implicitly using the likelihood ratio between a learnable target model and a fixed reference model, drawing parallels with the philosophy of Direct Preference Optimization (DPO). Unlike GANs, this parameterization eliminates the need for joint training of generator and discriminator networks, allowing for direct, efficient, and effective finetuning of a well-trained model to its full potential beyond the limits of MLE. DDO can be performed iteratively in a self-play manner for progressive model refinement, with each round requiring less than 1\% of pretraining epochs. Our experiments demonstrate the effectiveness of DDO by significantly advancing the previous SOTA diffusion model EDM, reducing FID scores from 1.79/1.58/1.96 to new records of 1.30/0.97/1.26 on CIFAR-10/ImageNet-64/ImageNet 512$\times$512 datasets without any guidance mechanisms, and by consistently improving both guidance-free and CFG-enhanced FIDs of visual autoregressive models on ImageNet 256$\times$256.

The ability to manipulate objects in desired configurations is a fundamental requirement for robots to complete various practical applications. While certain goals can be achieved by picking and placing the objects of interest directly, object reorientation is needed for precise placement in most of the tasks. In such scenarios, the object must be reoriented and re-positioned into intermediate poses that facilitate accurate placement at the target pose. To this end, we propose a reorientation planning method, ReorientDiff, that utilizes a diffusion model-based approach. The proposed method employs both visual inputs from the scene, and goal-specific language prompts to plan intermediate reorientation poses. Specifically, the scene and language-task information are mapped into a joint scene-task representation feature space, which is subsequently leveraged to condition the diffusion model. The diffusion model samples intermediate poses based on the representation using classifier-free guidance and then uses gradients of learned feasibility-score models for implicit iterative pose-refinement. The proposed method is evaluated using a set of YCB-objects and a suction gripper, demonstrating a success rate of 95.2% in simulation. Overall, we present a promising approach to address the reorientation challenge in manipulation by learning a conditional distribution, which is an effective way to move towards generalizable object manipulation. More results can be found on our website: https://utkarshmishra04.github.io/ReorientDiff.

We present DiffCollage, a compositional diffusion model that can generate large content by leveraging diffusion models trained on generating pieces of the large content. Our approach is based on a factor graph representation where each factor node represents a portion of the content and a variable node represents their overlap. This representation allows us to aggregate intermediate outputs from diffusion models defined on individual nodes to generate content of arbitrary size and shape in parallel without resorting to an autoregressive generation procedure. We apply DiffCollage to various tasks, including infinite image generation, panorama image generation, and long-duration text-guided motion generation. Extensive experimental results with a comparison to strong autoregressive baselines verify the effectiveness of our approach.

We consider guiding denoising diffusion models with general differentiable loss functions in a plug-and-play fashion, enabling controllable generation without additional training. This paradigm, termed Loss-Guided Diffusion (LGD), can easily be integrated into all diffusion models and leverage various efficient samplers. Despite the benefits, the resulting guidance term is, unfortunately, an intractable integral and needs to be approximated. Existing methods compute the guidance term based on a point estimate. However, we show that such approaches have significant errors over the scale of the approximations. To address this issue, we propose a Monte Carlo method that uses multiple samples from a suitable distribution to reduce bias. Our method is effective in various synthetic and real-world settings, including image super-resolution, text or label-conditional image generation, and controllable motion synthesis. Notably, we show how our method can be applied to control a pretrained motion diffusion model to follow certain paths and avoid obstacles that are proven challenging to prior methods.

In this work we approach the dual optimal reach-safe control problem using sparse approximations of Koopman operator. Matrix approximation of Koopman operator needs to solve a least-squares (LS) problem in the lifted function space, which is computationally intractable for fine discretizations and high dimensions. The state transitional physical meaning of the Koopman operator leads to a sparse LS problem in this space. Leveraging this sparsity, we propose an efficient method to solve the sparse LS problem where we reduce the problem dimension dramatically by formulating the problem using only the non-zero elements in the approximation matrix with known sparsity pattern. The obtained matrix approximation of the operators is then used in a dual optimal reach-safe problem formulation where a linear program with sparse linear constraints naturally appears. We validate our proposed method on various dynamical systems and show that the computation time for operator approximation is greatly reduced with high precision in the solutions.

Multi-marginal optimal transport (MOT) is a generalization of optimal transport to multiple marginals. Optimal transport has evolved into an important tool in many machine learning applications, and its multi-marginal extension opens up for addressing new challenges in the field of machine learning. However, the usage of MOT has been largely impeded by its computational complexity which scales exponentially in the number of marginals. Fortunately, in many applications, such as barycenter or interpolation problems, the cost function adheres to structures, which has recently been exploited for developing efficient computational methods. In this work we derive computational bounds for these methods. In particular, with $m$ marginal distributions supported on $n$ points, we provide a $ \mathcal{\tilde O}(d(\mathcal{T})m n^{w(G)+1}\epsilon^{-2})$ bound for a $\epsilon$-accuracy when the problem is associated with a graph that can be factored as a junction tree with diameter $d(\mathcal{T})$ and tree-width $w(G)$. For the special case of the Wasserstein barycenter problem, which corresponds to a star-shaped tree, our bound is in alignment with the existing complexity bound for it.

We study multi-marginal optimal transport problems from a probabilistic graphical model perspective. We point out an elegant connection between the two when the underlying cost for optimal transport allows a graph structure. In particular, an entropy regularized multi-marginal optimal transport is equivalent to a Bayesian marginal inference problem for probabilistic graphical models with the additional requirement that some of the marginal distributions are specified. This relation on the one hand extends the optimal transport as well as the probabilistic graphical model theories, and on the other hand leads to fast algorithms for multi-marginal optimal transport by leveraging the well-developed algorithms in Bayesian inference. Several numerical examples are provided to highlight the results.

Temporal-difference and Q-learning play a key role in deep reinforcement learning, where they are empowered by expressive nonlinear function approximators such as neural networks. At the core of their empirical successes is the learned feature representation, which embeds rich observations, e.g., images and texts, into the latent space that encodes semantic structures. Meanwhile, the evolution of such a feature representation is crucial to the convergence of temporal-difference and Q-learning. In particular, temporal-difference learning converges when the function approximator is linear in a feature representation, which is fixed throughout learning, and possibly diverges otherwise. We aim to answer the following questions: When the function approximator is a neural network, how does the associated feature representation evolve? If it converges, does it converge to the optimal one? We prove that utilizing an overparameterized two-layer neural network, temporal-difference and Q-learning globally minimize the mean-squared projected Bellman error at a sublinear rate. Moreover, the associated feature representation converges to the optimal one, generalizing the previous analysis of Cai et al. (2019) in the neural tangent kernel regime, where the associated feature representation stabilizes at the initial one. The key to our analysis is a mean-field perspective, which connects the evolution of a finite-dimensional parameter to its limiting counterpart over an infinite-dimensional Wasserstein space. Our analysis generalizes to soft Q-learning, which is further connected to policy gradient.

Despite the empirical success of the actor-critic algorithm, its theoretical understanding lags behind. In a broader context, actor-critic can be viewed as an online alternating update algorithm for bilevel optimization, whose convergence is known to be fragile. To understand the instability of actor-critic, we focus on its application to linear quadratic regulators, a simple yet fundamental setting of reinforcement learning. We establish a nonasymptotic convergence analysis of actor- critic in this setting. In particular, we prove that actor-critic finds a globally optimal pair of actor (policy) and critic (action-value function) at a linear rate of convergence. Our analysis may serve as a preliminary step towards a complete theoretical understanding of bilevel optimization with nonconvex subproblems, which is NP-hard in the worst case and is often solved using heuristics.

More than half of all cancer patients receive radiotherapy in their treatment process. However, our understanding of abnormal transcriptional responses to radiation remains poor. In this study, we employ an extended definition of Ollivier-Ricci curvature based on LI-Wasserstein distance to investigate genes and biological processes associated with ionizing radiation (IR) and ultraviolet radiation (UV) exposure using a microarray dataset. Gene expression levels were modeled on a gene interaction topology downloaded from the Human Protein Reference Database (HPRD). This was performed for IR, UV, and mock datasets, separately. The difference curvature value between IR and mock graphs (also between UV and mock) for each gene was used as a metric to estimate the extent to which the gene responds to radiation. We found that in comparison of the top 200 genes identified from IR and UV graphs, about 20~30% genes were overlapping. Through gene ontology enrichment analysis, we found that the metabolic-related biological process was highly associated with both IR and UV radiation exposure.