This is a PyTorch implementation of several normalizing flows, including a variational autoencoder. It is used in the articles A Gradient Based Strategy for Hamiltonian Monte Carlo Hyperparameter Optimization and Resampling Base Distributions of Normalizing Flows.

• Planar Flow (Rezende & Mohamed, 2015)
• Radial Flow (Rezende & Mohamed, 2015)
• NICE (Dinh et al., 2014)
• Real NVP (Dinh et al., 2016)
• Glow (Kingma & Dhariwal, 2018)
• Masked Autoregressive Flow (Papamakarios et al., 2017)
• Neural Spline Flow (Durkan et al., 2019)
• Circular Neural Spline Flow (Rezende et al., 2020)
• Residual Flow (Chen et al., 2019)
• Stochastic Normalizing Flows (Wu et al., 2020)

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

The latest version of the package can be installed via pip

pip install --upgrade git+https://github.com/VincentStimper/normalizing-flows.git

If you want to use a GPU, make sure that PyTorch is set up correctly by 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

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 normflow as nf

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

# Define list of flows
num_layers = 16
flows = []
for i in range(num_layers):
    # Neural network with two hidden layers having 32 units each
    # Last layer is initialized by zeros making training more stable
    param_map = nf.nets.MLP([1, 32, 32, 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=1024)

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

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