# Limits of Confidence in Diffusion > Source: > Published: 2026-10-02 00:00:00+00:00 [content type paper](https://machinelearning.apple.com/research/)published October 2026 Limits of Confidence in Diffusion AuthorsRuss Webb, Amitis Shidani, Alice Bizeul, Dan Busbridge Discrete diffusion, including remasking and uniform-state samplers, generate a sequence by writing multiple token positions per step, drawing each from a per-position distribution and choosing which positions to write from those same distributions. For domains of general interest (pixels, phonemes, or words) there are inherent dependencies between tokens. 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. On ScanAndAdd, a synthetic task whose joint distribution is available in closed form, we verify that every group of two or more undetermined positions a confidence ranking writes is dependent, and measure the generated distribution to be 29× the sampling-noise floor total variation while per-sample metrics are 1.0. Unmasking On-Policy Distillation: Where It Helps, Where It Hurts, and Why July 9, 2026[research area Methods and Algorithms](https://machinelearning.apple.com/research/?domain=Methods%20and%20Algorithms), [research area Speech and Natural Language Processing](https://machinelearning.apple.com/research/?domain=Speech%20and%20Natural%20Language%20Processing) On-policy distillation offers dense, per-token supervision for training reasoning models; however, it remains unclear under which conditions this signal is beneficial and under which it is detrimental. Which teacher model should be used, and in the case of self-distillation, which specific context should serve as the supervisory signal? Does the optimal choice vary from one token to the next? At present, addressing these questions typically… Position Prediction as an Effective Pre-training Strategy July 11, 2022[research area Methods and Algorithms](https://machinelearning.apple.com/research/?domain=Methods%20and%20Algorithms)[conference ICML](https://machinelearning.apple.com/research/?event=ICML) Transformers have gained increasing popularity in a wide range of applications, including Natural Language Processing (NLP), Computer Vision and Speech Recognition, because of their powerful representational capacity. However, harnessing this representational capacity effectively requires a large amount of data, strong regularization, or both, to mitigate overfitting. Recently, the power of the Transformer has been unlocked by self-supervised…