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Generative Modeling by Estimating Gradients of the Data Distribution

This repo contains the official implementation for the NeurIPS 2019 paper Generative Modeling by Estimating Gradients of the Data Distribution,

by Yang Song and Stefano Ermon. Stanford AI Lab.

Note: The method has been greatly stabilized by the subsequent work Improved Techniques for Training Score-Based Generative Models (code) and more recently extended by Score-Based Generative Modeling through Stochastic Differential Equations (code). This codebase is therefore not recommended for new projects anymore.

We describe a new method of generative modeling based on estimating the derivative of the log density function (a.k.a., Stein score) of the data distribution. We first perturb our training data by different Gaussian noise with progressively smaller variances. Next, we estimate the score function for each perturbed data distribution, by training a shared neural network named the Noise Conditional Score Network (NCSN) using score matching. We can directly produce samples from our NSCN with annealed Langevin dynamics.


  • PyTorch

  • PyYAML

  • tqdm

  • pillow

  • tensorboardX

  • seaborn

Running Experiments

Project Structure is the common gateway to all experiments. Type python --help to get its usage description.

usage: [-h] [--runner RUNNER] [--config CONFIG] [--seed SEED]
               [--run RUN] [--doc DOC] [--comment COMMENT] [--verbose VERBOSE]
               [--test] [--resume_training] [-o IMAGE_FOLDER]

optional arguments:
  -h, --help            show this help message and exit
  --runner RUNNER       The runner to execute
  --config CONFIG       Path to the config file
  --seed SEED           Random seed
  --run RUN             Path for saving running related data.
  --doc DOC             A string for documentation purpose
  --verbose VERBOSE     Verbose level: info | debug | warning | critical
  --test                Whether to test the model
  --resume_training     Whether to resume training
  -o IMAGE_FOLDER, --image_folder IMAGE_FOLDER
                        The directory of image outputs

There are four runner classes.

  • AnnealRunner The main runner class for experiments related to NCSN and annealed Langevin dynamics.
  • BaselineRunner Compared to AnnealRunner, this one does not anneal the noise. Instead, it uses a single fixed noise variance.
  • ScoreNetRunner This is the runner class for reproducing the experiment of Figure 1 (Middle, Right)
  • ToyRunner This is the runner class for reproducing the experiment of Figure 2 and Figure 3.

Configuration files are stored in configs/. For example, the configuration file of AnnealRunner is configs/anneal.yml. Log files are commonly stored in run/logs/doc_name, and tensorboard files are in run/tensorboard/doc_name. Here doc_name is the value fed to option --doc.


The usage of is quite self-evident. For example, we can train an NCSN by running

python --runner AnnealRunner --config anneal.yml --doc cifar10

Then the model will be trained according to the configuration files in configs/anneal.yml. The log files will be stored in run/logs/cifar10, and the tensorboard logs are in run/tensorboard/cifar10.


Suppose the log files are stored in run/logs/cifar10. We can produce samples to folder samples by running

python --runner AnnealRunner --test -o samples


We provide pretrained checkpoints Extract the file to the root folder. You should be able to produce samples like the following using this checkpoint.

Dataset Sampling procedure
CelebA Celeba


Please refer to Appendix B.2 of our paper for details on hyperparameters and model selection. When computing inception and FID scores, we first generate images from our model, and use the official code from OpenAI and the original code from TTUR authors to obtain the scores.


Large parts of the code are derived from this Github repo (the official implementation of the sliced score matching paper)

If you find the code / idea inspiring for your research, please consider citing the following

  title={Generative Modeling by Estimating Gradients of the Data Distribution},
  author={Song, Yang and Ermon, Stefano},
  booktitle={Advances in Neural Information Processing Systems},

and / or

  author    = {Yang Song and
               Sahaj Garg and
               Jiaxin Shi and
               Stefano Ermon},
  title     = {Sliced Score Matching: {A} Scalable Approach to Density and Score
  booktitle = {Proceedings of the Thirty-Fifth Conference on Uncertainty in Artificial
               Intelligence, {UAI} 2019, Tel Aviv, Israel, July 22-25, 2019},
  pages     = {204},
  year      = {2019},
  url       = {},


Noise Conditional Score Networks (NeurIPS 2019, Oral)








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