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Status: Archive (code is provided as-is, no updates expected)

Improve Variational Inference with Inverse Autoregressive Flow

Code for reproducing key results in the paper Improving Variational Inference with Inverse Autoregressive Flow by Diederik P. Kingma, Tim Salimans, Rafal Jozefowicz, Xi Chen, Ilya Sutskever, and Max Welling.


  1. Make sure that recent versions installed of:

    • Python (version 2.7 or higher)
    • Numpy (e.g. pip install numpy)
    • Theano (e.g. pip install Theano)
  2. Set floatX = float32 in the [global] section of Theano config (usually ~/.theanorc). Alternatively you could prepend THEANO_FLAGS=floatX=float32 to the python commands below.

  3. Clone this repository, e.g.:

git clone
  1. Download the CIFAR-10 dataset (get the Python version) and create an environment variable CIFAR10_PATH that points to the subdirectory with CIFAR-10 data. For example:
export CIFAR10_PATH="$HOME/cifar-10"

Syntax of


python with problem=cifar10 n_z=32 n_h=64 depths=[2,2,2] margs.depth_ar=1 margs.posterior=down_iaf2_NL margs.kl_min=0.25

problem is the problem (dataset) to train on. I only tested cifar10 for this release.

n_z is the number of stochastic featuremaps in each layer.

n_h is the number of deterministic featuremaps used throughout the model.

depths is an array of integers that denotes the depths of the levels in the model. Each level is a sequence of layers. Each subsequent level operates over spatially smaller featuremaps. In case of CIFAR-10, the first level operates over 16x16 featuremaps, the second over 8x8 featuremaps, etc.

Some possible choices for margs.posterior are:

  • up_diag: bottom-up factorized Gaussian
  • up_iaf1_nl: bottom-up IAF, mean-only perturbation
  • up_iaf2_nl: bottom-up IAF
  • down_diag: top-down factorized Gaussian
  • down_iaf1_nl: top-down IAF, mean-only perturbation
  • down_iaf2_nl: top-down IAF

margs.depth_ar is the number of hidden layers within IAF, and can be any non-negative integer.

margs.kl_min: the minimum information constraint. Should be a non-negative float (where 0 is no constraint).

Results of Table 3

(3.28 bits/dim)

python with problem=cifar10 n_h=160 depths=[10,10] margs.depth_ar=2 margs.posterior=down_iaf2_nl margs.prior=diag margs.kl_min=0.25

More instructions will follow.

Multi-GPU TensorFlow implementation


Make sure that recent versions installed of:

  • Python (version 2.7 or higher)
  • TensorFlow
  • tqdm

CIFAR10_PATH environment variable should point to the dataset location.

Syntax of

Training script:

python --logdir <logdir> --hpconfig depth=1,num_blocks=20,kl_min=0.1,learning_rate=0.002,batch_size=32 --num_gpus 8 --mode train

It will run the training procedure on a given number of GPUs. Model checkpoints will be stored in <logdir>/train directory along with TensorBoard summaries that are useful for monitoring and debugging issues.

Evaluation script:

python --logdir <logdir> --hpconfig depth=1,num_blocks=20,kl_min=0.1,learning_rate=0.002,batch_size=32 --num_gpus 1 --mode eval_test

It will run the evaluation on the test set using a single GPU and will produce TensorBoard summary with the results and generated samples.

To start TensorBoard:

tensorboard --logdir <logdir>

For the description of hyper-parameters, take a look at get_default_hparams function in

Loading from the checkpoint

The best IAF model trained on CIFAR-10 reached 3.15 bits/dim when evaluated with a single sample. With 10,000 samples, the estimation of log likelihood is 3.111 bits/dim. The checkpoint is available at link. Steps to use it:

  • download the file
  • create directory <logdir>/train/ and copy the checkpoint there
  • run the following command:
python --logdir <logdir> --hpconfig depth=1,num_blocks=20,kl_min=0.1,learning_rate=0.002,batch_size=32 --num_gpus 1 --mode eval_test

The script will run the evaluation on the test set and generate samples stored in TensorFlow events file that can be accessed using TensorBoard.


Code for reproducing key results in the paper "Improving Variational Inference with Inverse Autoregressive Flow"








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