Efficient Generative Modeling beyond Memoryless Diffusion via Adjoint Schrödinger Bridge Matching

2026-02-17

AI Summary

This work addresses the inefficiencies of conventional diffusion models, whose memoryless forward processes lead to curved sampling trajectories, noisy score targets, and suboptimal computational efficiency. To overcome these limitations, the authors propose the Adjoint Schrödinger Bridge Matching (ASBM) framework, which employs a two-stage learning strategy: first constructing a Schrödinger bridge forward dynamics from a data-to-energy-sampling perspective, and then using the resulting optimal coupling to supervise the backward generative process. This approach breaks free from the reliance on memoryless mechanisms, enabling—for the first time—the recovery of high-dimensional optimal transport trajectories in a non-Markovian setting. By integrating optimal transport matching losses with distillation techniques, ASBM achieves higher-fidelity image generation in fewer steps and successfully distills into a single-step generator, demonstrating the efficacy of trajectory optimization.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Learning to Search
• Machine Learning: Deep Generative Models & Autoencoders

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Diffusion models often yield highly curved trajectories and noisy score targets due to an uninformative, memoryless forward process that induces independent data-noise coupling. We propose Adjoint Schrödinger Bridge Matching (ASBM), a generative modeling framework that recovers optimal trajectories in high dimensions via two stages. First, we view the Schrödinger Bridge (SB) forward dynamic as a coupling construction problem and learn it through a data-to-energy sampling perspective that transports data to an energy-defined prior. Then, we learn the backward generative dynamic with a simple matching loss supervised by the induced optimal coupling. By operating in a non-memoryless regime, ASBM produces significantly straighter and more efficient sampling paths. Compared to prior works, ASBM scales to high-dimensional data with notably improved stability and efficiency. Extensive experiments on image generation show that ASBM improves fidelity with fewer sampling steps. We further showcase the effectiveness of our optimal trajectory via distillation to a one-step generator.

Problem

• diffusion models
• memoryless forward process
• noisy score targets
• curved trajectories
• generative modeling

Innovation

• Schrödinger Bridge
• generative modeling
• optimal transport
• non-memoryless diffusion
• trajectory distillation