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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.

Composable building blocks of SurVAE flows include:

  • Bijective: Invertible deterministic transformations. The usual building blocks in normalizing flows.
  • Stochastic: Stochastic transformations with stochastic inverses. VAEs are an important example.
  • Surjective (Gen.): Deterministic transformations in the generative direction with a stochastic right-inverse in the inference direction.
  • Surjective (Inf.): Deterministic transformations in the inference direction with a stochastic right-inverse in the generative direction.

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.

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),
             ])

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)
             ])

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),
             ])

Acknowledgements

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

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