  Microcanonical gradient descent is a sampling procedure for energy-based
models allowing for efficient sampling of distributions in high dimension. It
works by transporting samples from a high-entropy distribution, such as
Gaussian white noise, to a low-energy region using gradient descent. We put
this model in the framework of normalizing flows, showing how it can often
overfit by losing an unnecessary amount of entropy in the descent. As a remedy,
we propose a mean-field microcanonical gradient descent that samples several
weakly coupled data points simultaneously, allowing for better control of the
entropy loss while paying little in terms of likelihood fit. We study these
models in the context of financial time series, illustrating the improvements
on both synthetic and real data.
