# LLaCO adds spherical noising and log-rank retention to diffusion language models

> Original title: LLaCO fixes this with a grounded theoretical design:

- Source: BAAI
- Published: 2026-11-03T14:03:01.000Z
- Bad Influence: https://badinfluence.news/items/ie12wwss0i9odehyftfoneqi9
- Original: https://x.com/BAAIBeijing/status/2117618554178592936

## Summary

LLaCO is a diffusion language model method that uses spherical noising, a geodesic interpolation toward a [MASK]-biased endpoint that avoids norm decay while keeping pretrained semantic biases. It also introduces Log-Rank Retention (Q_log), which measures rank decay on a logarithmic scale to focus on top candidates, and trajectory reallocation, which concentrates compute where token identities shift.

## Post

LLaCO fixes this with a grounded theoretical design:

Spherical Noising: Geodesic interpolation toward a [MASK]-biased endpoint, eliminating norm decay while preserving pretrained semantic biases.

Log-Rank Retention (Q_log): Measuring rank decay on a logarithmic scale to focus strictly on top candidates.

Trajectory Reallocation: Concentrating compute dynamically where token identities actually shift.

![](https://badinfluence.news/api/img-proxy?u=https%3A%2F%2Fpbs.twimg.com%2Fmedia%2FHWKztVOasAArHOx.jpg&mode=thumb&exp=1793923200&sig=1008dc21aa046981)