normflows: A PyTorch Package for Normalizing Flows

This is a PyTorch implementation of normalizing flows. Many popular flow architectures are implemented, see the list below. The package can be easily installed via pip. The basic usage is described here, and a full documentation is available as well. There are several sample use cases implemented in the examples folder, including Glow, a VAE, and a Residual Flow.

Implemented Flows

Note that Neural Spline Flows with circular and non-circular coordinates are supported as well.

Installation

The latest version of the package can be installed via pip

pip install normflows

At least Python 3.7 is required. If you want to use a GPU, make sure that PyTorch is set up correctly by following the instructions at the PyTorch website.

To run the example notebooks clone the repository first

git clone https://github.com/VincentStimper/normalizing-flows.git

and then install the dependencies.

pip install -r requirements_examples.txt

Usage

A normalizing flow consists of a base distribution, defined in nf.distributions.base, and a list of flows, given in nf.flows. Let's assume our target is a 2D distribution. We pick a diagonal Gaussian base distribution, which is the most popular choice. Our flow shall be a Real NVP model and, therefore, we need to define a neural network for computing the parameters of the affine coupling map. One dimension is used to compute the scale and shift parameter for the other dimension. After each coupling layer we swap their roles.

import normflows as nf

# Define 2D Gaussian base distribution
base = nf.distributions.base.DiagGaussian(2)

# Define list of flows
num_layers = 32
flows = []
for i in range(num_layers):
    # Neural network with two hidden layers having 64 units each
    # Last layer is initialized by zeros making training more stable
    param_map = nf.nets.MLP([1, 64, 64, 2], init_zeros=True)
    # Add flow layer
    flows.append(nf.flows.AffineCouplingBlock(param_map))
    # Swap dimensions
    flows.append(nf.flows.Permute(2, mode='swap'))

Once they are set up, we can define a nf.NormalizingFlow model. If the target density is available, it can be added to the model to be used during training. Sample target distributions are given in nf.distributions.target.

# If the target density is not given
model = nf.NormalizingFlow(base, flows)

# If the target density is given
target = nf.distributions.target.TwoMoons()
model = nf.NormalizingFlow(base, flows, target)

The loss can be computed with the methods of the model and minimized.

# When doing maximum likelihood learning, i.e. minimizing the forward KLD
# with no target distribution given
loss = model.forward_kld(x)

# When minimizing the reverse KLD based on the given target distribution
loss = model.reverse_kld(num_samples=512)

# Optimization as usual
loss.backward()
optimizer.step()

As more extensive version of this example is given as a notebook, which can directly be opened in Colab. There, we apply a Real NVP model to a bimodal target distribution and obtain the following results.

In another example, we apply a Neural Spline Flow model to a distribution defined on a cylinder. The resulting density is visualized below.

For more illustrative examples of how to use the package see the examples directory. More advanced experiments can be done with the scripts listed in the repository about resampled base distributions, see its experiments folder.

Used by

The package has been used in several research papers, which are listed below.

Andrew Campbell, Wenlong Chen, Vincent Stimper, José Miguel Hernández-Lobato, and Yichuan Zhang. A gradient based strategy for Hamiltonian Monte Carlo hyperparameter optimization. In Proceedings of the 38th International Conference on Machine Learning, pp. 1238–1248. PMLR, 2021.

Code available on GitHub.

Vincent Stimper, Bernhard Schölkopf, José Miguel Hernández-Lobato. Resampling Base Distributions of Normalizing Flows. In Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, volume 151, pp. 4915–4936, 2022.

Code available on GitHub.

Laurence I. Midgley, Vincent Stimper, Gregor N. C. Simm, Bernhard Schölkopf, José Miguel Hernández-Lobato. Flow Annealed Importance Sampling Bootstrap. ArXiv, abs/2208.01893, 2022.

Code available on GitHub.

Moreover, the boltzgen package has been build upon normflows.