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Diffusion Probabilistic Models (DPMs) have emerged as a powerful class of deep generative models, achieving remarkable performance in image synthesis tasks. However, these models face challenges in terms of widespread adoption due to their…
Classifier guidance -- using the gradients of an image classifier to steer the generations of a diffusion model -- has the potential to dramatically expand the creative control over image generation and editing. However, currently…
In recent years we have witnessed a growth in mathematics for deep learning, which has been used to solve inverse problems of partial differential equations (PDEs). However, most deep learning-based inversion methods either require paired…
Despite remarkable progress in autoregressive language models, alternative generative paradigms beyond left-to-right generation are still being actively explored. Discrete diffusion models, with the capacity for parallel generation, have…
Alternating Direction Method of Multipliers (ADMM) algorithm has been widely adopted for solving the distributed optimization problem (DOP). In this paper, a new distributed parallel ADMM algorithm is proposed, which allows the agents to…
We propose a novel deterministic sampling method to approximate a target distribution $\rho^*$ by minimizing the kernel discrepancy, also known as the Maximum Mean Discrepancy (MMD). By employing the general \emph{energetic variational…
Score-based diffusion models, while achieving remarkable empirical performance, often suffer from low sampling speed, due to extensive function evaluations needed during the sampling phase. Despite a flurry of recent activities towards…
Diffusion models have achieved remarkable success, yet their training remains inefficient due to a severe optimization bottleneck, which we term Representation Degradation. As noise levels increase, the outputs of the trained model exhibit…
Alternating Direction Method of Multipliers (ADMM) has recently been proposed as a potential alternative optimizer to the Stochastic Gradient Descent(SGD) for deep learning problems. This is because ADMM can solve gradient vanishing and…
Stochastic gradient descent (SGD) is a widely adopted iterative method for optimizing differentiable objective functions. In this paper, we propose and discuss a novel approach to scale up SGD in applications involving non-convex functions…
Diffusion models are powerful generative models but suffer from slow sampling, often taking 1000 sequential denoising steps for one sample. As a result, considerable efforts have been directed toward reducing the number of denoising steps,…
Diffusion models have emerged as powerful generative priors for solving PDE-constrained inverse problems. Compared to end-to-end approaches relying on massive paired datasets, explicitly decoupling the prior distribution of physical…
Recent years have witnessed the rapid progress and broad application of diffusion probabilistic models (DPMs). Sampling from DPMs can be viewed as solving an ordinary differential equation (ODE). Despite the promising performance, the…
We propose, analyze, and test new iterative solvers for large-scale systems of linear algebraic equations arising from the finite element discretization of reduced optimality systems defining the finite element approximations to the…
Diffusion distillation is central to accelerating image and video generation, yet existing methods are fundamentally limited by the denoising process, where step reduction has largely saturated. Partial timestep low-resolution generation…
Diffusion models have demonstrated exceptional capabilities in generating high-fidelity images but typically suffer from inefficient sampling. Many solver designs and noise scheduling strategies have been proposed to dramatically improve…
Recent diffusion distillation methods have achieved remarkable progress, enabling high-quality ${\sim}4$-step sampling for large-scale text-conditional image and video diffusion models. However, further reducing the number of sampling steps…
Optimizing conflicting molecular properties while strictly adhering to complex 3D structural constraints constitutes a challenging Constrained Multi-Objective Optimization Problem (CMOP). Traditional Evolutionary Algorithms (EAs) destroy…
Diffusion models generate high-quality images but require dozens of forward passes. We introduce Distribution Matching Distillation (DMD), a procedure to transform a diffusion model into a one-step image generator with minimal impact on…
Moment-based distributionally robust optimization (DRO) provides an optimization framework to integrate statistical information with traditional optimization approaches. Under this framework, one assumes that the underlying joint…