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.

翻译：扩散模型常因采用非信息性、无记忆的前向过程而引入独立的数据-噪声耦合，导致轨迹高度弯曲且得分目标噪声显著。我们提出伴随薛定谔桥匹配（ASBM），一种通过两阶段恢复高维最优轨迹的生成建模框架。首先，我们将薛定谔桥（SB）前向动态视为耦合构建问题，通过数据到能量的采样视角进行学习，将数据传输至能量定义的先验分布。随后，我们通过由诱导最优耦合监督的简单匹配损失来学习后向生成动态。通过在非无记忆机制下运行，ASBM 产生了显著更平直、更高效的采样路径。与先前工作相比，ASBM 可扩展至高维数据，并显著提升了稳定性和效率。在图像生成上的大量实验表明，ASBM 能以更少的采样步骤提高保真度。我们进一步通过将最优轨迹蒸馏至单步生成器，展示了其有效性。