Learning normalizing flows from Entropy-Kantorovich potentials
This work addresses a computational bottleneck in training normalizing flows for machine learning practitioners, though it appears incremental as it builds on existing optimal transport and flow methods.
The authors tackled the problem of learning continuous normalizing flows by reformulating it using entropy-regularized optimal transport, casting flows as gradients of scalar potentials, which enabled training without explicit flow computation and allowed easy recovery post-training.
We approach the problem of learning continuous normalizing flows from a dual perspective motivated by entropy-regularized optimal transport, in which continuous normalizing flows are cast as gradients of scalar potential functions. This formulation allows us to train a dual objective comprised only of the scalar potential functions, and removes the burden of explicitly computing normalizing flows during training. After training, the normalizing flow is easily recovered from the potential functions.