Variational Schrödinger Momentum Diffusion
This work addresses scalability challenges in generative diffusion processes for applications like time series and image generation, representing an incremental improvement over existing momentum-based methods.
The paper tackles the high training costs and scalability issues of momentum Schrödinger Bridge methods by introducing variational Schrödinger momentum diffusion (VSMD), which uses linearized forward score functions to eliminate simulated forward trajectories and achieves competitive results in time series and image generation.
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.