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score_models

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A repository to store state of the art score model architectures

// repository documentation

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# Score Models for Pytorch

[![PyPI version](https://badge.fury.io/py/score_models.svg)](https://badge.fury.io/py/score_models)
[![codecov](https://codecov.io/gh/AlexandreAdam/torch_score_models/branch/master/graph/badge.svg)](https://codecov.io/gh/AlexandreAdam/torch_score_models)

A storage for score-based models. The `ScoreModel` interface gives access to the following utilities
- Simple initialisation of MLP, NCSN++ and DDPM neural network architectures
- A fit method to train the score model on a dataset using Denoising Score Matching (DSM: see [Vincent 2011](https://www.iro.umontreal.ca/~vincentp/Publications/DenoisingScoreMatching_NeuralComp2011.pdf)).
- A sampling method based on an Euler-Maruyama discretisation of an SDE. 
- A simple interface to train an energy model using DSM

This repository is mainly intended for personal use. 
You might also want to refer to the original implementation at [https://github.com/yang-song/score_sde](https://github.com/yang-song/score_sde).

## Installation

To install the package, you can use pip:

```bash
pip install score_models
```

## Usage

### ScoreModel

The `ScoreModel` class is the main interface for training and using score models, defined as

```math
\mathbf{s}_\theta(t, \mathbf{x}) \equiv \nabla_\mathbf{x} \log p_t(\mathbf{x}) = \frac{1}{\sigma(t)} f_\theta (t, \mathbf{x})$$
```

where $\sigma(t)$ is the standard deviation of the perturbation kernel $`p_t(\mathbf{x} \mid \mathbf{x}_0)`$
of an SDE and $f_\theta : [0, 1] \times\mathbb{R}^d \to \mathbb{R}^d$ is a neural network for $\mathbf{x} \in \mathbb{R}^d$.

The `ScoreModel` class extends the `torch.nn.Module` class. Example usage:

```python
from score_models import ScoreModel, EnergyModel, NCSNpp, MLP, DDPM

# B is the batch size
# C is the input channels
# dimensions are the spatial dimensions (e.g. [28, 28] for MNIST)

# Create a ScoreModel instance with Yang Song's NCSN++ architecture and the VESDE
net = NCSNpp(channels=C, dimensions=len(dimensions), nf=128, ch_mult=[2, 2, 2, 2])
model = ScoreModel(model=net, sigma_min=1e-2, sigma_max=50, device="cuda")
# ... or the VPSDE
model = ScoreModel(model=net, beta_min=1e-2, beta_max=20, device="cuda")

# NN Architectures support a Unet with 1D convolutions for time series input data
net = NCSNpp(channels=C, nf=128, ch_mult=[2, 2, 2, 2], dimensions=1)
# ... or 3D convolutions for videos/voxels
net = NCSNpp(channels=1, nf=128, ch_mult=[2, 2, 2, 2], attention=False, dimensions=3)
# You can also use a simpler MLP architecture (dimensions=0)
net = MLP(dimensions=C, layers=4, units=100)
# ... or Jonathan Ho's DDPM architecture
net = DDPM(channels=1, nf=128, ch_mult=[2, 2, 2, 2])

# Train the score model, and save its weight in checkpoints_directory
model.fit(dataset, epochs=100, batch_size=B, learning_rate=1e-4, checkpoints_directory=checkpoints_directory)

# Generate samples from the trained model (steps is the number of Euler-Maruyama steps)
samples = model.sample(shape=[B, *dimensions], steps=1000)

# Compute the score for a given input
score = model.score(t, x)

# Initialise the score model and its neural network from a path to a checkpoint directory 
model = ScoreModel(checkpoints_directory=checkpoints_directory)
```

### EnergyModel

The `EnergyModel` class works in pretty much the same way as `ScoreModel`, but implements the score via the 
automatic differentation of an energy model
```math
E_\theta(t, \mathbf{x}) = \frac{1}{2 \sigma(t)} \lVert \mathbf{x} - f_\theta (t, \mathbf{x}) \rVert_2^ 2
```

This is to say that the score is defined as
```math
\mathbf{s}_\theta (t, \mathbf{x}) = - \nabla_\mathbf{x} E_\theta(t, \mathbf{x}) 
```

**Note**: When using the MLP architecture, the energy model can be constructed more efficiently as the output of the
neural network by specifying `nn_is_energy` in the hyperparameters of the MLP, which will modify the neural network 
architecture to be a function $f_\theta: [0, 1] \times\mathbb{R}^d \to \mathbb{R}$ instead of $f_\theta: [0, 1] \times\mathbb{R}^d \to \mathbb{R}^d$. An `output_activation` like `relu` 
can also be specified to make the energy positive or bounded from below.

### Training Parameters

When training the model using the `fit` method, you can provide various parameters to customize the training process. Some important parameters include:

- `dataset`: The training dataset (`torch.utils.data.Dataset`).
- `epochs`: The number of training epochs.
- `learning_rate`: The learning rate for the ADAM optimizer.
- `batch_size`: The batch size for training.
- `checkpoints_directory`: The directory to save model checkpoints (default: None).
- `seed`: The random seed for numpy and torch.

Refer to the method's docstring or the class definition for more details on available parameters.

## Citations

If you use this package in your research, please consider citing the following papers:

```bibtex
@inproceedings{Song2021,
  title={Score-Based Generative Modeling through Stochastic Differential Equations},
  author={Yang Song and Jascha Sohl-Dickstein and Diederik P Kingma and Abhishek Kumar and Stefano Ermon and Ben Poole},
  booktitle={International Conference on Learning Representations},
  year={2021},
  url={https://openreview.net/forum?id=PxTIG12RRHS}
}
```

```bibtex
@article{Adam2022,
       author = {{Adam}, Alexandre and {Coogan}, Adam and {Malkin}, Nikolay and {Legin}, Ronan and {Perreault-Levasseur}, Laurence and {Hezaveh}, Yashar and {Bengio}, Yoshua},
        title = "{Posterior samples of source galaxies in strong gravitational lenses with score-based priors}",
      journal = {arXiv e-prints},
         year = 2022,
        month = nov,
          eid = {arXiv:2211.03812},
          doi = {10.48550/arXiv.2211.03812},
archivePrefix = {arXiv},
       eprint = {2211.03812},
 primaryClass = {astro-ph.IM},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2022arXiv221103812A},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
```
```bibtex
@article{Legin2023,
       author = {{Legin}, Ronan and {Adam}, Alexandre and {Hezaveh}, Yashar and {Perreault-Levasseur}, Laurence},
        title = "{Beyond Gaussian Noise: A Generalized Approach to Likelihood Analysis with Non-Gaussian Noise}",
      journal = {\apjl},
     keywords = {James Webb Space Telescope, Hubble Space Telescope, Non-Gaussianity, Astronomy image processing, Observational astronomy, Bayesian statistics, CCD observation, Cosmic rays, Posterior distribution, Neural networks, Astronomy data analysis, Computational methods, 2291, 761, 1116, 2306, 1145, 1900, 207, 329, 1926, 1933, 1858, 1965, Astrophysics - Instrumentation and Methods for Astrophysics},
         year = 2023,
        month = jun,
       volume = {949},
       number = {2},
          eid = {L41},
        pages = {L41},
          doi = {10.3847/2041-8213/acd645},
archivePrefix = {arXiv},
       eprint = {2302.03046},
 primaryClass = {astro-ph.IM},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2023ApJ...949L..41L},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}
```

```bibtex
@inproceedings{Ho2020,
    author      = {Ho, Jonathan and Jain, Ajay and Abbeel, Pieter},
    booktitle   = {Advances in Neural Information Processing Systems},
    editor      = {H. Larochelle and M. Ranzato and R. Hadsell and M.F. Balcan and H. Lin},
    pages       = {6840--6851},
    publisher   = {Curran Associates, Inc.},
    title       = {Denoising Diffusion Probabilistic Models},
    url         = {https://proceedings.neurips.cc/paper/2020/file/4c5bcfec8584af0d967f1ab10179ca

4b-Paper.pdf},
    volume      = {33},
    year        = {2020}
}
```

This package is licensed under the MIT License.

score_models

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