# Guaranteed Conditional Diffusion: 3D Block-based Models for Scientific Data Compression

arXiv: https://arxiv.org/abs/2502.12951 · HTML: https://mlsanity.com/paper/2502.12951/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 21 of its 30 references that are in the map.
- First posted on arXiv 18 Feb 2025.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 21 of 21)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [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)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Variational image compression with a scale hyperprior](https://mlsanity.com/paper/1802.01436/) (2018)
- [End-to-end Optimized Image Compression](https://mlsanity.com/paper/1611.01704/) (2016)
- [Joint Autoregressive and Hierarchical Priors for Learned Image Compression](https://mlsanity.com/paper/1809.02736/) (2018)
- [Autoregressive Diffusion Models](https://mlsanity.com/paper/2110.02037/) (2021)
- [Lossy Image Compression with Conditional Diffusion Models](https://mlsanity.com/paper/2209.06950/) (2022)
- [Towards image compression with perfect realism at ultra-low bitrates](https://mlsanity.com/paper/2310.10325/) (2023)
- [Swin2SR: SwinV2 Transformer for Compressed Image Super-Resolution and Restoration](https://mlsanity.com/paper/2209.11345/) (2022)
- [Lossy Image Compression with Foundation Diffusion Models](https://mlsanity.com/paper/2404.08580/) (2024)
- [SZ3: A Modular Framework for Composing Prediction-Based Error-Bounded Lossy Compressors](https://mlsanity.com/paper/2111.02925/) (2021)
- [Efficient Video Compression via Content-Adaptive Super-Resolution](https://mlsanity.com/paper/2104.02322/) (2021)
- [Correcting Diffusion-Based Perceptual Image Compression with Privileged End-to-End Decoder](https://mlsanity.com/paper/2404.04916/) (2024)
- [Machine Learning Techniques for Data Reduction of CFD Applications](https://mlsanity.com/paper/2404.18063/) (2024)

## Built on by (most cited first, 3 of 3)

- [PET Image Denoising via Text-Guided Diffusion: Integrating Anatomical Priors through Text Prompts](https://mlsanity.com/paper/2502.21260/) (2025)
- [Generative Latent Diffusion for Efficient Spatiotemporal Data Reduction](https://mlsanity.com/paper/2507.02129/) (2025)
- [Neural Residual Modeling for Scientific Data Compression under Guaranteed Error Bounds](https://mlsanity.com/paper/2609.23185/) (2026)

## Abstract (arXiv)

This paper proposes a new compression paradigm -- Guaranteed Conditional Diffusion with Tensor Correction (GCDTC) -- for lossy scientific data compression. The framework is based on recent conditional diffusion (CD) generative models, and it consists of a conditional diffusion model, tensor correction, and error guarantee. Our diffusion model is a mixture of 3D conditioning and 2D denoising U-Net. The approach leverages a 3D block-based compressing module to address spatiotemporal correlations in structured scientific data. Then, the reverse diffusion process for 2D spatial data is conditioned on the ``slices'' of content latent variables produced by the compressing module. After training, the denoising decoder reconstructs the data with zero noise and content latent variables, and thus it is entirely deterministic. The reconstructed outputs of the CD model are further post-processed by our tensor correction and error guarantee steps to control and ensure a maximum error distortion, which is an inevitable requirement in lossy scientific data compression. Our experiments involving two datasets generated by climate and chemical combustion simulations show that our framework outperforms standard convolutional autoencoders and yields competitive compression quality with an existing scientific data compression algorithm.