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We present Deep Compression Autoencoder (DC-AE), a new family of autoencoder models for accelerating high-resolution diffusion models. Existing autoencoder models have demonstrated impressive results at a moderate spatial compression ratio…

High Order DG methods with Riemann solver based interface numerical flux functions offer an interesting dispersion dissipation behaviour: dispersion errors are very low for a broad range of scales, while dissipation errors are very low for…

The slow inference process of image diffusion models significantly degrades interactive user experiences. To address this, we introduce Diffusion Preview, a novel paradigm employing rapid, low-step sampling to generate preliminary outputs…

Diffusion-based image-to-image (I2I) translation excels in high-fidelity generation but suffers from slow sampling in state-of-the-art Diffusion Bridge Models (DBMs), often requiring dozens of function evaluations (NFEs). We introduce…

Efficient inference is a critical challenge in deep generative modeling, particularly as diffusion models grow in capacity and complexity. While increased complexity often improves accuracy, it raises compute costs, latency, and memory…

The rare-event sampling problem has long been the central limiting factor in molecular dynamics (MD), especially in biomolecular simulation. Recently, diffusion models such as BioEmu have emerged as powerful equilibrium samplers that…

Diffusion-based generative models are extremely effective in generating high-quality images, with generated samples often surpassing the quality of those produced by other models under several metrics. One distinguishing feature of these…

Discrete flow models (DFMs) have been proposed to learn the data distribution on finite state space, offering a flexible framework as an alternative to discrete diffusion models. A line of recent work has studied samplers for discrete…

In this paper, we present a novel spectral renormalization exponential integrator method for solving gradient flow problems. Our method is specifically designed to simultaneously satisfy discrete analogues of the energy dissipation laws and…

Guided diffusion is a technique for conditioning the output of a diffusion model at sampling time without retraining the network for each specific task. One drawback of diffusion models, however, is their slow sampling process. Recent…

We introduced and analyzed robust recovery-based a posteriori error estimators for various lower order finite element approximations to interface problems in [9, 10], where the recoveries of the flux and/or gradient are implicit (i.e.,…

Diffusion Inverse Solvers (DIS) are designed to sample from the conditional distribution $p_{\theta}(X_0|y)$, with a predefined diffusion model $p_{\theta}(X_0)$, an operator $f(\cdot)$, and a measurement $y=f(x'_0)$ derived from an unknown…

We propose a high order numerical homogenization method for dissipative ordinary differential equations (ODEs) containing two time scales. Essentially, only first order homogenized model globally in time can be derived. To achieve a high…

The choice of prior is central to solving ill-posed imaging inverse problems, making it essential to select one consistent with the measurements $y$ to avoid severe bias. In Bayesian inverse problems, this could be achieved by evaluating…

It has been recognized that the data generated by the denoising diffusion probabilistic model (DDPM) improves adversarial training. After two years of rapid development in diffusion models, a question naturally arises: can better diffusion…

Ordinary differential equations (ODEs) are widely used to describe dynamical systems in science, but identifying parameters that explain experimental measurements is challenging. In particular, although ODEs are differentiable and would…

Score-based diffusion models have emerged as powerful techniques for generating samples from high-dimensional data distributions. These models involve a two-phase process: first, injecting noise to transform the data distribution into a…

Diffusion-based solvers for partial differential equations (PDEs) are often bottle-necked by slow gradient-based test-time optimization routines that use PDE residuals for loss guidance. They additionally suffer from optimization…

In this paper, we propose high order numerical methods to solve a 2D advection diffusion equation, in the highly oscillatory regime. We use an integrator strategy that allows the construction of arbitrary high-order schemes {leading} to an…

The aim of this work is to apply a semi-implicit (SI) strategy within a Rosenbrock-type and IMEX linear multistep (LM) framework to a sequence of 1D time-dependent partial differential equations (PDEs) with high order spatial derivatives.…