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For several decades, image restoration remains an active research topic in low-level computer vision and hence new approaches are constantly emerging. However, many recently proposed algorithms achieve state-of-the-art performance only at…

Diffusion models are powerful generative models that map noise to data using stochastic processes. However, for many applications such as image editing, the model input comes from a distribution that is not random noise. As such, diffusion…

Due to the high flexibility and remarkable performance, low-rank approximation methods has been widely studied for color image denoising. However, those methods mostly ignore either the cross-channel difference or the spatial variation of…

We propose Diffusion-Sharpening, a fine-tuning approach that enhances downstream alignment by optimizing sampling trajectories. Existing RL-based fine-tuning methods focus on single training timesteps and neglect trajectory-level alignment,…

Randomized neural networks (RNN) are a variation of neural networks in which the hidden-layer parameters are fixed to randomly assigned values and the output-layer parameters are obtained by solving a linear system by least squares. This…

In the field of Robot Learning, the complex mapping between high-dimensional observations such as RGB images and low-level robotic actions, two inherently very different spaces, constitutes a complex learning problem, especially with…

A nonlinear diffusion equation, interpreted as a Wasserstein gradient flow, is numerically solved in one space dimension using a higher-order minimizing movement scheme based on the BDF (backward differentiation formula) discretization. In…

We present a framework leveraging a novel variant of the model-based diffusion algorithm to minimize the time required for a redundant dual-arm robot configuration to follow a desired relative Cartesian path. Our prior work proposed a…

First-order methods like stochastic gradient descent(SGD) are recently the popular optimization method to train deep neural networks (DNNs), but second-order methods are scarcely used because of the overpriced computing cost in getting the…

While deep neural networks (NN) significantly advance image compressed sensing (CS) by improving reconstruction quality, the necessity of training current CS NNs from scratch constrains their effectiveness and hampers rapid deployment.…

We develop a cut Discontinuous Galerkin method (cutDGM) for a diffusion-reaction equation in a bulk domain which is coupled to a corresponding equation on the boundary of the bulk domain. The bulk domain is embedded into a structured,…

Diffusion models have recently shown promise in offline RL. However, these methods often suffer from high training costs and slow convergence, particularly when using transformer-based denoising backbones. While several optimization…

Denoising diffusion bridge models (DDBMs) are a powerful variant of diffusion models for interpolating between two arbitrary paired distributions given as endpoints. Despite their promising performance in tasks like image translation, DDBMs…

In this research, we propose a novel denoising diffusion model based on shortest-path modeling that optimizes residual propagation to enhance both denoising efficiency and quality. Drawing on Denoising Diffusion Implicit Models (DDIM) and…

This chapter offers a comprehensive introduction to the least-squares neural network (LSNN) method introduced in [14,16], for solving scalar first-order hyperbolic partial differential equations, specifically linear advection-reaction…

We propose a distributed cubic regularization of the Newton method for solving (constrained) empirical risk minimization problems over a network of agents, modeled as undirected graph. The algorithm employs an inexact, preconditioned Newton…

We study the problem of minimizing a sum of convex objective functions where the components of the objective are available at different nodes of a network and nodes are allowed to only communicate with their neighbors. The use of…

Deep learning forms a hierarchical network structure for representation of multiple input features. The adaptive structural learning method of Deep Belief Network (DBN) can realize a high classification capability while searching the…

We propose an adaptive diffusion mechanism to optimize a global cost function in a distributed manner over a network of nodes. The cost function is assumed to consist of a collection of individual components. Diffusion adaptation allows the…

Establishing reliable correspondences is crucial for all registration tasks, including 2D image registration, 3D point cloud registration, and 2D-3D image-to-point cloud registration. However, these tasks are often complicated by challenges…