# Micro-Diffusion Compression - Binary Tree Tweedie Denoising for Online Probability Estimation

arXiv: https://arxiv.org/abs/2603.08771 · HTML: https://mlsanity.com/paper/2603.08771/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 26 references that are in the map.
- First posted on arXiv 9 Mar 2026.

## Builds on (most cited first, 6 of 6)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Language Modeling Is Compression](https://mlsanity.com/paper/2309.10668/) (2023)
- [FineZip : Pushing the Limits of Large Language Models for Practical Lossless Text Compression](https://mlsanity.com/paper/2409.17141/) (2024)
- [Nacrith: Neural Lossless Compression via Ensemble Context Modeling and High-Precision CDF Coding](https://mlsanity.com/paper/2602.19626/) (2026)

## Abstract (arXiv)

We present Midicoth, a lossless compression system that introduces a micro-diffusion denoising layer for improving probability estimates produced by adaptive statistical models. In compressors such as Prediction by Partial Matching (PPM), probability estimates are smoothed by a prior to handle sparse observations. When contexts have been seen only a few times, this prior dominates the prediction and produces distributions that are significantly flatter than the true source distribution, leading to compression inefficiency. Midicoth addresses this limitation by treating prior smoothing as a shrinkage process and applying a reverse denoising step that corrects predicted probabilities using empirical calibration statistics. To make this correction data-efficient, the method decomposes each byte prediction into a hierarchy of binary decisions along a bitwise tree. This converts a single 256-way calibration problem into a sequence of binary calibration tasks, enabling reliable estimation of correction terms from relatively small numbers of observations. The denoising process is applied in multiple successive steps, allowing each stage to refine residual prediction errors left by the previous one. The micro-diffusion layer operates as a lightweight post-blend calibration stage applied after all model predictions have been combined, allowing it to correct systematic biases in the final probability distribution. Midicoth combines five fully online components: an adaptive PPM model, a long-range match model, a trie-based word model, a high-order context model, and the micro-diffusion denoiser applied as the final stage.