Unfortunately the intuition and the math proofs so far suggest that autoregressive training is learning the joint distribution of probabilistic streams of tokens much better than diffision models do or will ever do. My intuitive take is that the conditional probability distribtion of decoder-only autoregressive models is at just the right level of complexity for probabilistic models to learn accurately enough. Intuitively (and simplifying things at the risk of breaking rigor), the diffusion (or masked models) have to occasionally issue tokens with less information and thus higher variance than a pure autoregressive model would have to do, so the joint distribution, ie the probability of the whole sentence/answer will be lower and thus diffusion models will never get precise enough. Of course, during generation the sampling techniques influence the above simplified idea dramatically and the typical randomized sampling for next token prediction is suboptimal and could be beaten by a carefully designed block diffusion sampler in principle in some contexts though I havent seen real examples of it yet. But the key ideas of the above scribbles are still valid: autoregresive models will always be better (or at least equal) probabilistic models of sequential data than diffusion models will be. So the diffusion models mostly offer a tradeoff for performance vs quality. Sometimes there is a lot of room for that tradeoff in practice.
From the mathematical point of view the literature is about the distinction between a "filtering" distribution and a "smoothing" distribution. The smoothing distribution is strictly more powerful.
In theory intuitively the smoothing distribution has access to all the information that the filtering distribution has and some additional information therefore has a minimum lower than the filtering distribution.
In practice, because the smoothing input space is much bigger, keeping the same number of parameters we may not reach a better score because with diffusion we are tackling a much harder problem (the whole problem), whereas with autoregressive models we are taking a shortcut which happens to probably be one that humans are probably biased too (communication evolved so that it can be serialized to be exchanged orally).
Although what you say about smoothing vs filtering is true in principle, for conditional generation of the eventual joint distribution starting from the same condition and using an autoregresive vs diffusive LLM, it is the smoothing distribution that has less power. In other words, during inference starting from J tokens and writing token number K is of course better with diffusion if you also have some given tokens after token K and up to the maximal token N. However, if your input is fixed (tokens up to J) and you have to predict those additional tokens (from J+1 to N), you are solving a harder problem and have a lower joint probability at the end of the inference for the full generated sequence from J+1 up to N.
I am still jetlagged and not sure what the most helpful reference would be. Maybe start from the block diffusion paper I recommended in a parallel thread and trace your way up/down from there. The logic leading to Eq 6 is a special case of such a math proof.
The human processing is still autoregressive, but using multiple parallel synchronized streams. There is no problem with such an approach and my best guess is that in the next year we will see many teams training models using such tricks for generating reasoning traces in parallel.
The main concern is taking a single probabilistic stream (eg a book) and comparing autoregressive modelling of it with a diffusive modelling of it.
