# Lossy Compression with Gaussian Diffusion

arXiv: https://arxiv.org/abs/2206.08889 · HTML: https://mlsanity.com/paper/2206.08889/

## Key facts

- Cited by 90 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion for compression and wireless, one of 14 directions in Diffusion models.
- Builds on 43 of its 69 references that are in the map.
- First posted on arXiv 17 Jun 2022.

## Placed in

- Diffusion models / [Diffusion for compression and wireless](https://mlsanity.com/diffusion/diffusion-for-compression-and-wireless/)

## Builds on (most cited first, 30 of 43)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Pixel Recurrent Neural Networks](https://mlsanity.com/paper/1601.06759/) (2016)
- [Vector Quantized Diffusion Model for Text-to-Image Synthesis](https://mlsanity.com/paper/2111.14822/) (2021)
- [SoundStream: An End-to-End Neural Audio Codec](https://mlsanity.com/paper/2107.03312/) (2021)
- [Big Transfer (BiT): General Visual Representation Learning](https://mlsanity.com/paper/1912.11370/) (2019)
- [End-to-end Optimized Image Compression](https://mlsanity.com/paper/1611.01704/) (2016)
- [Score-based Generative Modeling in Latent Space](https://mlsanity.com/paper/2106.05931/) (2021)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [High-Fidelity Generative Image Compression](https://mlsanity.com/paper/2006.09965/) (2020)
- [Lossy Image Compression with Compressive Autoencoders](https://mlsanity.com/paper/1703.00395/) (2017)
- [Score-Based Generative Modeling with Critically-Damped Langevin Diffusion](https://mlsanity.com/paper/2112.07068/) (2021)
- [Generative Adversarial Networks for Extreme Learned Image Compression](https://mlsanity.com/paper/1804.02958/) (2018)
- [Gotta Go Fast When Generating Data with Score-Based Models](https://mlsanity.com/paper/2105.14080/) (2021)
- [Rethinking Lossy Compression: The Rate-Distortion-Perception Tradeoff](https://mlsanity.com/paper/1901.07821/) (2019)
- [Generalized Sliced Wasserstein Distances](https://mlsanity.com/paper/1902.00434/) (2019)
- [On Fast Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2106.00132/) (2021)
- [Nonlinear Transform Coding](https://mlsanity.com/paper/2007.03034/) (2020)
- [Learning to Efficiently Sample from Diffusion Probabilistic Models](https://mlsanity.com/paper/2106.03802/) (2021)
- [DiffuseVAE: Efficient, Controllable and High-Fidelity Generation from Low-Dimensional Latents](https://mlsanity.com/paper/2201.00308/) (2022)

## Built on by (most cited first, 30 of 90)

- [Imagic: Text-Based Real Image Editing with Diffusion Models](https://mlsanity.com/paper/2210.09276/) (2022)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [A Survey on Generative Diffusion Model](https://mlsanity.com/paper/2209.02646/) (2022)
- [Lossy Image Compression with Conditional Diffusion Models](https://mlsanity.com/paper/2209.06950/) (2022)
- [Contrastive Energy Prediction for Exact Energy-Guided Diffusion Sampling in Offline Reinforcement Learning](https://mlsanity.com/paper/2304.12824/) (2023)
- [Editing Implicit Assumptions in Text-to-Image Diffusion Models](https://mlsanity.com/paper/2303.08084/) (2023)
- [Neural Video Compression with Feature Modulation](https://mlsanity.com/paper/2402.17414/) (2024)
- [Towards image compression with perfect realism at ultra-low bitrates](https://mlsanity.com/paper/2310.10325/) (2023)
- [Improving Statistical Fidelity for Neural Image Compression with Implicit Local Likelihood Models](https://mlsanity.com/paper/2301.11189/) (2023)
- [Blurring Diffusion Models](https://mlsanity.com/paper/2209.05557/) (2022)
- [Multi-Realism Image Compression with a Conditional Generator](https://mlsanity.com/paper/2212.13824/) (2022)
- [Text + Sketch: Image Compression at Ultra Low Rates](https://mlsanity.com/paper/2307.01944/) (2023)
- [Towards Extreme Image Compression with Latent Feature Guidance and Diffusion Prior](https://mlsanity.com/paper/2404.18820/) (2024)
- [High-Fidelity Image Compression with Score-based Generative Models](https://mlsanity.com/paper/2305.18231/) (2023)
- [GSURE-Based Diffusion Model Training with Corrupted Data](https://mlsanity.com/paper/2305.13128/) (2023)
- [A Residual Diffusion Model for High Perceptual Quality Codec Augmentation](https://mlsanity.com/paper/2301.05489/) (2023)
- [Enhancing Diffusion-Based Image Synthesis with Robust Classifier Guidance](https://mlsanity.com/paper/2208.08664/) (2022)
- [StableCodec: Taming One-Step Diffusion for Extreme Image Compression](https://mlsanity.com/paper/2506.21977/) (2025)
- [Extreme Generative Image Compression by Learning Text Embedding from Diffusion Models](https://mlsanity.com/paper/2211.07793/) (2022)
- [Idempotence and Perceptual Image Compression](https://mlsanity.com/paper/2401.08920/) (2024)
- [Compressed Image Generation with Denoising Diffusion Codebook Models](https://mlsanity.com/paper/2502.01189/) (2025)
- [Compression with Bayesian Implicit Neural Representations](https://mlsanity.com/paper/2305.19185/) (2023)
- [Lossy Compression with Pretrained Diffusion Models](https://mlsanity.com/paper/2501.09815/) (2025)
- [Modality-Agnostic Variational Compression of Implicit Neural Representations](https://mlsanity.com/paper/2301.09479/) (2023)
- [Ultra Lowrate Image Compression with Semantic Residual Coding and Compression-aware Diffusion](https://mlsanity.com/paper/2505.08281/) (2025)
- [Just One Byte (per gradient): A Note on Low-Bandwidth Decentralized Language Model Finetuning Using Shared Randomness](https://mlsanity.com/paper/2306.10015/) (2023)
- [Controlling Rate, Distortion, and Realism: Towards a Single Comprehensive Neural Image Compression Model](https://mlsanity.com/paper/2405.16817/) (2024)
- [Do Perceptually Aligned Gradients Imply Adversarial Robustness?](https://mlsanity.com/paper/2207.11378/) (2022)
- [EGIC: Enhanced Low-Bit-Rate Generative Image Compression Guided by Semantic Segmentation](https://mlsanity.com/paper/2309.03244/) (2023)
- [Compression with Exact Error Distribution for Federated Learning](https://mlsanity.com/paper/2310.20682/) (2023)

## Abstract (arXiv)

We consider a novel lossy compression approach based on unconditional diffusion generative models, which we call DiffC. Unlike modern compression schemes which rely on transform coding and quantization to restrict the transmitted information, DiffC relies on the efficient communication of pixels corrupted by Gaussian noise. We implement a proof of concept and find that it works surprisingly well despite the lack of an encoder transform, outperforming the state-of-the-art generative compression method HiFiC on ImageNet 64x64. DiffC only uses a single model to encode and denoise corrupted pixels at arbitrary bitrates. The approach further provides support for progressive coding, that is, decoding from partial bit streams. We perform a rate-distortion analysis to gain a deeper understanding of its performance, providing analytical results for multivariate Gaussian data as well as theoretic bounds for general distributions. Furthermore, we prove that a flow-based reconstruction achieves a 3 dB gain over ancestral sampling at high bitrates.