Stochastic Normalizing Flows
This work addresses challenges in probabilistic modeling and sampling for machine learning researchers, presenting an incremental extension of existing normalizing flow methods.
The authors tackled the problem of maximum likelihood estimation and variational inference by extending continuous normalizing flows with stochastic differential equations (SDEs), treating Brownian motion as a latent variable to enable efficient training of neural SDEs for sampling from data distributions and optimizing hyperparameters in stochastic MCMC.
We introduce stochastic normalizing flows, an extension of continuous normalizing flows for maximum likelihood estimation and variational inference (VI) using stochastic differential equations (SDEs). Using the theory of rough paths, the underlying Brownian motion is treated as a latent variable and approximated, enabling efficient training of neural SDEs as random neural ordinary differential equations. These SDEs can be used for constructing efficient Markov chains to sample from the underlying distribution of a given dataset. Furthermore, by considering families of targeted SDEs with prescribed stationary distribution, we can apply VI to the optimization of hyperparameters in stochastic MCMC.