# Apple — Limits of Confidence in Diffusion

- Company: Apple (apple.com)
- Announced: 2026-10-02
- Category: research-paper
- Coverage: not counted
- Announcement: yes
- Group: announcements
- Source: https://machinelearning.apple.com/research/limits-confidence-diffusion
- Record: https://forck.live/items/15791-limits-of-confidence-in-diffusion
- Subject: Machine Learning Research

Apple researchers prove that discrete diffusion models using per-position distributions (including remasking and uniform-state samplers) cannot match the training distribution when the tokens they write are dependent, and that per-position marginals alone cannot detect such dependence. On a synthetic task, they measure the generated distribution's total variation to be 29 times the sampling-noise floor.

## Evidence

Verbatim from https://machinelearning.apple.com/research/limits-confidence-diffusion:

> We show that a step matches the training distribution only when the positions it writes are conditionally independent given the tokens already fixed, that no product of per-position distributions can match a dependent group, and that per-position distributions do not determine whether a group is dependent: two joint distributions can have identical per-position marginals while differing in which combinations of values occur.

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