| Abstract: |
| The diffusion model has shown remarkable success in computer vision, but it remains unclear whether the ODE-based probability flow or the SDE-based diffusion model is more superior and under what circumstances. Comparing the two is challenging due to dependencies on data distributions, score training, and other numerical issues. In this talk, we will discuss a mathematical approach for this problem by considering two limiting scenarios: the zero diffusion (ODE) case and the large diffusion case. We will demonstrate that the time distribution of the score training error will determine the optimal dynamics in terms of minimizing the sampling error in the continuous-time setting. Numerical validation of this phenomenon is provided using various benchmark distributions, as well as realistic datasets. |
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