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This paper presents a multiscale approach to efficiently compute approximate optimal transport plans between point sets. It is particularly well-suited for point sets that are in high-dimensions, but are close to being intrinsically…
We introduce Deep Set Linearized Optimal Transport, an algorithm designed for the efficient simultaneous embedding of point clouds into an $L^2-$space. This embedding preserves specific low-dimensional structures within the Wasserstein…
Sampling from high-dimensional distributions is a fundamental problem in statistical research and practice. However, great challenges emerge when the target density function is unnormalized and contains isolated modes. We tackle this…
Differential dynamic programming (DDP) is a popular technique for solving nonlinear optimal control problems with locally quadratic approximations. However, existing DDP methods are not designed for stochastic systems with unknown…
Mesh deformation plays a pivotal role in many 3D vision tasks including dynamic simulations, rendering, and reconstruction. However, defining an efficient discrepancy between predicted and target meshes remains an open problem. A prevalent…
We propose a distributed algorithm for solving the optimization problem Basis Pursuit (BP). BP finds the least L1-norm solution of the underdetermined linear system Ax = b and is used, for example, in compressed sensing for reconstruction.…
Denoising diffusion probabilistic models (DDPMs) have emerged as competitive generative models yet brought challenges to efficient sampling. In this paper, we propose novel bilateral denoising diffusion models (BDDMs), which take…
We present a class of diffusion-based algorithms to draw samples from high-dimensional probability distributions given their unnormalized densities. Ideally, our methods can transport samples from a Gaussian distribution to a specified…
Solving high-dimensional Bayesian inverse problems (BIPs) with the variational inference (VI) method is promising but still challenging. The main difficulties arise from two aspects. First, VI methods approximate the posterior distribution…
Wasserstein 1 optimal transport maps provide a natural correspondence between points from two probability distributions, $\mu$ and $\nu$, which is useful in many applications. Available algorithms for computing these maps do not appear to…
We propose the stochastic optimal path which solves the classical optimal path problem by a probability-softening solution. This unified approach transforms a wide range of DP problems into directed acyclic graphs in which all paths follow…
We present an algorithm to estimate fast and accurate depth maps from light fields via a sparse set of depth edges and gradients. Our proposed approach is based around the idea that true depth edges are more sensitive than texture edges to…
The generation of 3D molecules requires simultaneously deciding the categorical features~(atom types) and continuous features~(atom coordinates). Deep generative models, especially Diffusion Models (DMs), have demonstrated effectiveness in…
Digital backpropagation (DBP) is one of the most effective techniques for compensating nonlinear distortions in coherent optical fiber communication systems. However, its practical application to wideband transmission remains limited by…
This paper presents a light-weight, high-quality texture synthesis algorithm that easily generalizes to other applications such as style transfer and texture mixing. We represent texture features through the deep neural activation vectors…
We propose the Binary Diffusion Probabilistic Model (BDPM), a generative framework specifically designed for data representations in binary form. Conventional denoising diffusion probabilistic models (DDPMs) assume continuous inputs, use…
Motivated by the computational difficulties incurred by popular deep learning algorithms for the generative modeling of temporal densities, we propose a cheap alternative which requires minimal hyperparameter tuning and scales favorably to…
We propose a diffusion approximation method to the continuous-state Markov Decision Processes (MDPs) that can be utilized to address autonomous navigation and control in unstructured off-road environments. In contrast to most…
Particle-based variational inference offers a flexible way of approximating complex posterior distributions with a set of particles. In this paper we introduce a new particle-based variational inference method based on the theory of…
The performance of optimization-based robot motion planning algorithms is highly dependent on the initial solutions, commonly obtained by running a sampling-based planner to obtain a collision-free path. However, these methods can be slow…