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Limits of Confidence in Diffusion
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.
Source and freshness
- Source
- machinelearning.apple.com
- Published
- Added to Yomu
Summaries are generated from the original by a language model. Check the original before relying on it.
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