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On the Asymptotic Mean Square Error Optimality of Diffusion Models

Implementation to reproduce the simulation results of

B. Fesl, B. Böck, F. Strasser, M. Baur, M. Joham, and W. Utschick, "On the Asymptotic Mean Square Error Optimality of Diffusion Models," 2024, arXiv preprint: 2403.02957.
Link to paper: https://arxiv.org/abs/2403.02957

Load data

Load data and pre-trained models from https://syncandshare.lrz.de/getlink/fiAsDStAV6i5FFJHyfhrcY/ (Passcode: Diffusion2024) and move it to the project's directory.

Information about required packages

Down below is a list of mandatory and optional packages with their versions, if a specific version is required.

Mandatory packages

  • conda-build
  • cudatoolkit=11.8
  • numpy
  • pytorch=2.0.1
  • torchvision=0.15.2=py310_cu118 (only if working with image data)
  • pytorch-cuda=11.8
  • scikit-learn
  • scipy
  • tqdm
  • pip
  • pytorch-fid==0.3
  • matplotlib

Optional packages (for jupyter notebooks or special script options)

  • seaborn
  • ipykernel
  • ray-core
  • ray-tune
  • ray-train
  • ray-dashboard

Common Usage

  1. Train and test a DPM-based denoiser on GPU
python dpm_denoiser.py -d cuda:0
  1. Load pre-trained model and evaluate it
python load_and_eval_dpm.py -d cuda:0
  1. Evaluate real-valued baselines (GMM-based CME and LS)
python baselines.py
  1. Evaluate complex-valued baseline with audio-data (GMM-based CME and LS)
python audio_gmm.py

Data Options

  1. rand_gmm
  2. MNIST_gmm
  3. FASHION_MNIST_gmm
  4. audio_gmm

Licenses

The diffusion model architecture is based upon the code from https://github.com/hojonathanho/diffusion.

The real-valued Gaussian mixture model implementation stems from https://scikit-learn.org/stable/modules/mixture.html and is covered by the following license:

BSD 3-Clause License

Copyright (c) 2007-2023 The scikit-learn developers. All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

  1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.

  2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.

  3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

The complex-valued extension of the Gaussian mixture model implementation stems from https://github.com/benediktfesl/GMM_cplx and is covered by the following license:

BSD 3-Clause License

Copyright (c) 2023 Benedikt Fesl. All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

  1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.

  2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.

  3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.