Efficient Generative Modeling beyond Memoryless Diffusion via Adjoint Schrödinger Bridge Matching

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.

Many programs that generate images learn to do so by reversing a noising process — starting from random static and gradually shaping it into a picture. Current methods add so much noise that all connection between the original image and the noise is lost, resulting in long, winding paths that require many steps to produce good results. We developed a method called Adjoint Schrödinger Bridge Matching (ASBM) that preserves meaningful links between images and their noisy versions. By finding the shortest route between them, our model learns straighter, more direct paths from noise to image. It does this in two stages: first learning how images optimally map to noise, then training a generator that efficiently reverses this mapping. Our method produces better images with fewer steps — and can even do it in a single step after distillation — making the generation process significantly faster and more practical.