变分薛定谔动量扩散
Variational Schrödinger Momentum Diffusion
AI总结：
提出变分薛定谔动量扩散（VSMD），利用线性化变分得分消除对前向轨迹模拟的依赖，结合临界阻尼变换稳定训练，在保持传输效率与可扩展性的同时，于时间序列和图像生成任务中取得有竞争力的结果。
摘要：
动量薛定谔桥（mSB）已成为加速生成扩散过程和降低传输成本的领先方法。然而，缺乏无模拟特性不可避免地导致高昂的训练成本并影响可扩展性。为了在传输特性和可扩展性之间取得权衡，我们引入了变分薛定谔动量扩散（VSMD），它采用线性化的前向得分函数（变分得分）来消除对模拟前向轨迹的依赖。我们的方法利用具有自适应传输优化变分得分的多变量扩散过程。此外，我们应用临界阻尼变换来稳定训练，消除了对速度和样本进行得分估计的需求。在理论上，我们证明了使用最优变分得分和动量扩散生成的样本的收敛性。实验结果表明，VSMD能高效生成各向异性形状，同时保持传输效率，优于过阻尼替代方案，并避免了复杂的去噪过程。我们的方法也能有效扩展到真实世界数据，在时间序列和图像生成中取得了有竞争力的结果。
英文摘要：
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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