arXiv subjects

Zilai Li

Publications and source records attributed to Zilai Li.

5 recordsLinked to original sources

arXiv2026

EMPURPLE: A Free Lunch for Diffusion Distillation based on the Information Bottleneck

Diffusion models achieve impressive image-generation quality but remain expensive at inference time. Diffusion distillation reduces sampling steps, yet many distilled models, including SDXL-Lightning and distribution matching distillation methods, suffer from degraded Fr\'echet Inception Distance (FID). We analyze this phenomenon through a PAC-style generalization bound. Our analysis suggests that aggressive early-step redirection of the velocity field makes the distillation target harder to learn, enlarging the train-test gap. As a result, early-step output distributions differ between training and inference, causing distribution mismatch in the intermediate noisy latent used as next-step inputs. We empirically validate this mechanism by showing reduced diversity in both intermediate features and final outputs. To address this issue, we propose EMPURPLE, a simple training-free method that recycles intermediate latents sampled from the original model. EMPURPLE is model-agnostic and improves FID by 7\% to 20\% across DMD2, Hyper-SD, FlashSD, and SDXL-Lightning. The repo is: https://github.com/TheLovesOfLadyPurple/Empurple-Training-Free-Algorithm-To-enhance-Diversity-of-The-Diffusion-Distillation-Model

cs.CV↗

arXiv2025

F-scheduler: illuminating the free-lunch design space for fast sampling of diffusion models

Diffusion models are the state-of-the-art generative models for high-resolution images, but sampling from pretrained models is computationally expensive, motivating interest in fast sampling. Although Free-U Net is a training-free enhancement for improving image quality, we find it ineffective under few-step ($<10$) sampling. We analyze the discrete diffusion ODE and propose F-scheduler, a scheduler designed for ODE solvers with Free-U Net. Our proposed scheduler consists of a special time schedule that does not fully denoise the feature to enable the use of the KL-term in the $\beta$-VAE decoder, and the schedule of a proper inference stage for modifying the U-Net skip-connection via Free-U Net. Via information theory, we provide insights into how the better scheduled ODE solvers for the diffusion model can outperform the training-based diffusion distillation model. The newly proposed scheduler is compatible with most of the few-step ODE solvers and can sample a 1024 x 1024-resolution image in 6 steps and a 512 x 512-resolution image in 5 steps when it applies to DPM++ 2m and UniPC, with an FID result that outperforms the SOTA distillation models and the 20-step DPM++ 2m solver, respectively. Codebase: https://github.com/TheLovesOfLadyPurple/F-scheduler

cs.GR↗

arXiv2022

Global Classical Solutions to the viscous two-phase flow model with slip Boundary Conditions in 3D Exterior Domains

We consider the two-phase flow model with slip boundary condition in a 3D exterior domains whose boundary is smooth. We establish the global existence of classical solutions of this system provided that the initial energy is suitably small. Moreover, the pressure has large oscillations and contains vacuum states when the initial pressure allows large oscillations and a vacuum. Finally, we also obtain the large-time behavior of the classical solutions.

math.AP↗

arXiv2021

On non-resistive limit of 1D MHD equations with no vacuum at infinity

In this paper, we consider the Cauchy problem for the one-dimensional compressible isentropic magnetohydrodynamic (MHD) equations with no vacuum at infinity, but the initial vacuum can be permitted inside the region. By deriving a priori $ν$ (resistivity coefficient)-independent estimates, we establish the non-resistive limit of the global strong solutions with large initial data. Moreover, as a by-product, the global well-posedness of strong solutions for both the compressible resistive MHD equations and non-resistive MHD equations are also established, respectively.

math.AP↗

arXiv2016

Global well-posedness for the 2D Boussinesq Equations with Zero Viscosity

We prove the global well-posedness of the two-dimensional Boussinesq equations with zero viscosity and positive diffusivity in bounded domains for rough initial data [ $u_{0}\in L^{2}$, $\text{curl}\,u_{0}\in L^{\infty}$ and $θ_{0}\in B^{2-2/p}_{q,p}$ with $p\in (1,\infty)$, $q\in (2,\infty)$ ]. Our method is based on the maximal regularity for heat equation.

math.AP↗