Probability-Flow ODE in Infinite-Dimensional Function Spaces
This work addresses inference speed for researchers and practitioners using infinite-dimensional diffusion models in function generation, representing an incremental improvement.
The authors tackled the problem of slow inference in infinite-dimensional diffusion models by deriving a probability-flow ODE for function spaces, which reduced the number of function evaluations while maintaining sample quality in tasks like PDE applications.
Recent advances in infinite-dimensional diffusion models have demonstrated their effectiveness and scalability in function generation tasks where the underlying structure is inherently infinite-dimensional. To accelerate inference in such models, we derive, for the first time, an analog of the probability-flow ODE (PF-ODE) in infinite-dimensional function spaces. Leveraging this newly formulated PF-ODE, we reduce the number of function evaluations while maintaining sample quality in function generation tasks, including applications to PDEs.