---
title: "Limits of Confidence in Diffusion"
description: "The post analyzes limitations of confidence-based ranking in discrete diffusion, where sequences are generated by writing multiple token positions per step from per-position distributions. It shows that a step matches the training distribution only when the written positions are conditionally independent given fixed tokens, and no product of per-position distributions can match a dependent group. Additionally, per-position distributions do not determine group dependence: two joint distributions can have identical per-position marginals but differ in value combinations. On the synthetic ScanAndAdd task, every group of two or more undetermined positions written by a confidence ranking is dependent, and the generated distribution is 29 times the sampling-noise floor in total variation, with per-sample metrics at 1.0. The post also includes updates on two related readings: on-policy distillation for reasoning models and self-supervised learning with Transformers."
---

# Limits of Confidence in Diffusion

[Apple](https://yomu.fyi/company/apple) · Oct 2, 2026

**Type:** Explainer

## Summary

The post analyzes limitations of confidence-based ranking in discrete diffusion, where sequences are generated by writing multiple token positions per step from per-position distributions. It shows that a step matches the training distribution only when the written positions are conditionally independent given fixed tokens, and no product of per-position distributions can match a dependent group. Additionally, per-position distributions do not determine group dependence: two joint distributions can have identical per-position marginals but differ in value combinations. On the synthetic ScanAndAdd task, every group of two or more undetermined positions written by a confidence ranking is dependent, and the generated distribution is 29 times the sampling-noise floor in total variation, with per-sample metrics at 1.0. The post also includes updates on two related readings: on-policy distillation for reasoning models and self-supervised learning with Transformers.

## Context

The post investigates the limits of confidence-based ranking in discrete diffusion, focusing on the conditional independence requirement for training distribution matching. It demonstrates that no product of per-position distributions can represent dependent groups and that per-position marginals do not determine joint dependence. These findings are validated on the synthetic ScanAndAdd task. Additionally, the post references related updates on on-policy distillation and Transformers.

## Takeaways

- A confidence-based discrete diffusion step matches the training distribution only when the positions it writes are conditionally independent given the tokens already fixed.
- No product of per-position distributions can represent a dependent group; identical per-position marginals can arise from different joint distributions, so marginals do not determine dependence.
- On the ScanAndAdd synthetic task, every group of two or more undetermined positions written by a confidence ranking is dependent, and the generated distribution deviates 29 times the sampling-noise floor in total variation, with per-sample metrics of 1.0.

## FAQ

### When does a discrete diffusion step match the training distribution?

It matches only when the written positions are conditionally independent given tokens already fixed. Otherwise, the per-position distributions cannot combine to match the true joint distribution.

### Can per-position distributions determine group dependence?

No. Two joint distributions can have identical per-position marginals but differ in which combinations of values occur, so marginals alone cannot determine dependence.

### What does the ScanAndAdd experiment demonstrate?

It shows that every group of multiple undetermined positions written by confidence ranking is dependent, and the generated distribution has a total variation distance 29 times the sampling-noise floor.

**Tags:** [Generative AI](https://yomu.fyi/topic/generative-ai), [Synthetic Data](https://yomu.fyi/topic/synthetic-data)

- Source: [Apple](https://machinelearning.apple.com/research/limits-confidence-diffusion)
- Source URL: https://machinelearning.apple.com/research/limits-confidence-diffusion
- Ingested by Yomu: 2026-10-02T21:00:06.377Z

[Read original post](https://machinelearning.apple.com/research/limits-confidence-diffusion)