SurVAE Flows

Official code for SurVAE Flows: Surjections to Bridge the Gap between VAEs and Flows
by Didrik Nielsen, Priyank Jaini, Emiel Hoogeboom, Ole Winther, Max Welling.

SurVAE Flows is a framework of composable transformations that extends the framework of normalizing flows.
SurVAE Flows make use of not only bijective transformations, but also surjective and stochastic transformations.
For more details, see the paper or check out this talk by Max Welling.

Contents

• /survae/: Code for the SurVAE library. See description below.
• /examples/: Runnable examples using the SurVAE library.
• /experiments/: Code to reproduce the experiments in the paper.

Pretrained models can be downloaded from releases.

The SurVAE Library

The SurVAE library is a Python package, built on top of PyTorch.
The SurVAE library allows straightforward construction of SurVAE flows.

Installation

In the folder containing setup.py, run

pip install .

Example 1: Normalizing Flow

We can construct a simple normalizing flow by stacking bijective transformations.
In this case, we model 2d data using a flow of 4 affine coupling layers.

import torch.nn as nn
from survae.flows import Flow
from survae.distributions import StandardNormal
from survae.transforms import AffineCouplingBijection, ActNormBijection, Reverse
from survae.nn.layers import ElementwiseParams

def net():
  return nn.Sequential(nn.Linear(1, 200), nn.ReLU(),
                       nn.Linear(200, 100), nn.ReLU(),
                       nn.Linear(100, 2), ElementwiseParams(2))

model = Flow(base_dist=StandardNormal((2,)),
             transforms=[
               AffineCouplingBijection(net()), ActNormBijection(2), Reverse(2),
               AffineCouplingBijection(net()), ActNormBijection(2), Reverse(2),
               AffineCouplingBijection(net()), ActNormBijection(2), Reverse(2),
               AffineCouplingBijection(net()), ActNormBijection(2),
             ])

See here for a runnable example.

Example 2: VAE

We can further build VAEs using stochastic transformations.
We here construct a simple VAE for binary images of shape (1,28,28), such as binarized MNIST.
We can easily extend this simple VAE by adding more layers to obtain e.g. hierarchical VAEs or VAEs with flow priors.
We can also use conditional flows in the encoder and/or decoder to obtain a more expressive VAE transformation.

from survae.flows import Flow
from survae.transforms import VAE
from survae.distributions import StandardNormal, ConditionalNormal, ConditionalBernoulli
from survae.nn.nets import MLP

encoder = ConditionalNormal(MLP(784, 2*latent_size,
                                hidden_units=[512,256],
                                activation='relu',
                                in_lambda=lambda x: 2 * x.view(x.shape[0], 784).float() - 1))
decoder = ConditionalBernoulli(MLP(latent_size, 784,
                                   hidden_units=[512,256],
                                   activation='relu',
                                   out_lambda=lambda x: x.view(x.shape[0], 1, 28, 28)))

model = Flow(base_dist=StandardNormal((latent_size,)),
             transforms=[
                VAE(encoder=encoder, decoder=decoder)
             ])

See here for a runnable example.

Example 3: Multi-Scale Augmented Flow

We can implement e.g. dequantization, augmentation and multi-scale flows using surjective transformations.
Here, we use these layers in a multi-scale augmented flow for (3,32,32) images such as CIFAR-10.

Notice that this makes use of 3 types of surjective layers:

1. Generative rounding: Implemented using UniformDequantization. Allows conversion to continuous variables. Useful for training continuous flows on ordinal discrete data.
2. Generative slicing: Implemented using Augment. Allows increasing dimensionality towards the latent space. Useful for constructing augmented normalizing flows.
3. Inference slicing: Implemented using Slice. Allows decreasing dimensionality towards the latent space. Useful for constructing multi-scale architectures.

import torch.nn as nn
from survae.flows import Flow
from survae.distributions import StandardNormal, StandardUniform
from survae.transforms import AffineCouplingBijection, ActNormBijection2d, Conv1x1
from survae.transforms import UniformDequantization, Augment, Squeeze2d, Slice
from survae.nn.layers import ElementwiseParams2d
from survae.nn.nets import DenseNet

def net(channels):
  return nn.Sequential(DenseNet(in_channels=channels//2,
                                out_channels=channels,
                                num_blocks=1,
                                mid_channels=64,
                                depth=8,
                                growth=16,
                                dropout=0.0,
                                gated_conv=True,
                                zero_init=True),
                        ElementwiseParams2d(2))

model = Flow(base_dist=StandardNormal((24,8,8)),
             transforms=[
               UniformDequantization(num_bits=8),
               Augment(StandardUniform((3,32,32)), x_size=3),
               AffineCouplingBijection(net(6)), ActNormBijection2d(6), Conv1x1(6),
               AffineCouplingBijection(net(6)), ActNormBijection2d(6), Conv1x1(6),
               AffineCouplingBijection(net(6)), ActNormBijection2d(6), Conv1x1(6),
               AffineCouplingBijection(net(6)), ActNormBijection2d(6), Conv1x1(6),
               Squeeze2d(), Slice(StandardNormal((12,16,16)), num_keep=12),
               AffineCouplingBijection(net(12)), ActNormBijection2d(12), Conv1x1(12),
               AffineCouplingBijection(net(12)), ActNormBijection2d(12), Conv1x1(12),
               AffineCouplingBijection(net(12)), ActNormBijection2d(12), Conv1x1(12),
               AffineCouplingBijection(net(12)), ActNormBijection2d(12), Conv1x1(12),
               Squeeze2d(), Slice(StandardNormal((24,8,8)), num_keep=24),
               AffineCouplingBijection(net(24)), ActNormBijection2d(24), Conv1x1(24),
               AffineCouplingBijection(net(24)), ActNormBijection2d(24), Conv1x1(24),
               AffineCouplingBijection(net(24)), ActNormBijection2d(24), Conv1x1(24),
               AffineCouplingBijection(net(24)), ActNormBijection2d(24), Conv1x1(24),
             ])

See here for a runnable example.

Acknowledgements

This code base builds on several other repositories. The biggest sources of inspiration are:

• https://github.com/bayesiains/nsf
• https://github.com/pclucas14/pytorch-glow
• https://github.com/karpathy/pytorch-made

Thanks to the authors of these and the many other useful repositories!