An Ordinary Differential Equation Sampler with Stochastic Start for Diffusion Bridge Models

2024-12-28

AI Summary

Existing diffusion bridge models for image inpainting and style transfer rely on stochastic differential equation (SDE) sampling, suffering from slow inference and initial-value singularity in the probability flow ODE—causing artifacts in early sampling steps and degrading both quality and efficiency. To address this, we propose a novel high-order ODE sampler for diffusion bridges with randomized starting points: it introduces a “randomized initialization + posterior sampling” mechanism to effectively mitigate ODE initial-value singularity; and integrates the Heun second-order solver to ensure trajectory smoothness and low discretization error—without requiring model retraining. The method is fully compatible with existing conditional diffusion bridge frameworks. On super-resolution, JPEG artifact removal, and Edges-to-Handbags tasks, it achieves significantly lower FID scores than state-of-the-art methods while reducing neural function evaluations (NFEs) by a large margin, all while preserving superior visual quality.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Diffusion bridge models have demonstrated promising performance in conditional image generation tasks, such as image restoration and translation, by initializing the generative process from corrupted images instead of pure Gaussian noise. However, existing diffusion bridge models often rely on Stochastic Differential Equation (SDE) samplers, which result in slower inference speed compared to diffusion models that employ high-order Ordinary Differential Equation (ODE) solvers for acceleration. To mitigate this gap, we propose a high-order ODE sampler with a stochastic start for diffusion bridge models. To overcome the singular behavior of the probability flow ODE (PF-ODE) at the beginning of the reverse process, a posterior sampling approach was introduced at the first reverse step. The sampling was designed to ensure a smooth transition from corrupted images to the generative trajectory while reducing discretization errors. Following this stochastic start, Heun's second-order solver is applied to solve the PF-ODE, achieving high perceptual quality with significantly reduced neural function evaluations (NFEs). Our method is fully compatible with pretrained diffusion bridge models and requires no additional training. Extensive experiments on image restoration and translation tasks, including super-resolution, JPEG restoration, Edges-to-Handbags, and DIODE-Outdoor, demonstrated that our sampler outperforms state-of-the-art methods in both visual quality and Frechet Inception Distance (FID).

Problem

• Diffusion Bridge Models
• Image Generation Efficiency
• SDE vs ODE Methods

Innovation

• Diffusion Bridge Model Optimization
• Heun's Second-order Method
• Image Quality Enhancement