提出VSMD方法，让扩散模型生成更快更稳，无需模拟轨迹。
Variational Schrödinger Momentum Diffusion
- 用可变得分函数替代模拟路径，降低训练开销。
- 生成异向形状效果好，比传统方法快且无需复杂去噪。
- 适合需要高效生成的真实数据场景，如图像与时间序列。
动量薛定谔桥（mSB）是加速生成扩散过程、降低传输成本的领先方法，但缺乏无需模拟的特性导致训练成本高，影响可扩展性。为在传输性能与可扩展性间取得平衡，本文提出变分薛定谔动量扩散（VSMD），采用线性化前向得分函数（变分得分）消除对模拟前向轨迹的依赖。该方法利用具有自适应优化传输特性的多变量扩散过程，并通过临界阻尼变换稳定训练，无需估计速度和样本的得分。理论上，我们证明了使用最优变分得分与动量扩散生成样本的收敛性。实验表明，VSMD能高效生成各向异性形状，保持传输有效性，优于过阻尼方法，且避免复杂去噪过程。该方法还能有效扩展至真实数据，在时间序列与图像生成任务中达到竞争力表现。
原文摘要 · Abstract (English)
The momentum Schrödinger Bridge (mSB) has emerged as a leading method for accelerating generative diffusion processes and reducing transport costs. However, the lack of simulation-free properties inevitably results in high training costs and affects scalability. To obtain a trade-off between transport properties and scalability, we introduce variational Schrödinger momentum diffusion (VSMD), which employs linearized forward score functions (variational scores) to eliminate the dependence on simulated forward trajectories. Our approach leverages a multivariate diffusion process with adaptively transport-optimized variational scores. Additionally, we apply a critical-damping transform to stabilize training by removing the need for score estimations for both velocity and samples. Theoretically, we prove the convergence of samples generated with optimal variational scores and momentum diffusion. Empirical results demonstrate that VSMD efficiently generates anisotropic shapes while maintaining transport efficacy, outperforming overdamped alternatives, and avoiding complex denoising processes. Our approach also scales effectively to real-world data, achieving competitive results in time series and image generation.
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