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Correct, diffusion LMs can edit their intermediate predictions, so "final" tokens aren't necessarily final. This is an exciting property because it allows models to correct errors in what's generated so far -- something that GPT-like models can't.

This editing is based on the Transformer's encoder property to predict token probabilities for __every__ token in a sequence, not just for [MASK]s. So when you input a sentence of three tokens `[MASK] cat barks`, Transformer will generate a probability distribution over the vocabulary for each of the three tokens, for free.

Now you can come up with many ways of how to decide whether you want to edit token or keep it as is. In the simplest case, take a new token if its probability higher than the original by some margin. In our example, say model returns the probability of the token "cat" on the second position as p_2("cat") = 0.3, while p_2("dog") = 0.6. We may want to replace "cat" with dog, and use it in the subsequent iterations.

Actual heuristics are slightly more complicated, but the base idea is this.

P.S. In order to teach LM not to just copy input unmasked tokens but to try to find a better replacement, your training objective should include replacing some % of input tokens with some other random token. Now you have part of the input masked, and part of the input corrupted, so the model can't blindly assume that all input tokens are here to stay.

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paulsmith a day ago | parent | next [-]

> say model returns the probability of the token "cat" on the second position as p_2("cat") = 0.3, while p_2("dog") = 0.6. We may want to replace "cat" with dog, and use it in the subsequent iterations.

Might one tradeoff of speed/quality be a tree "search" for better outcomes by branching on logit choices? If a diffusion model is so much faster overall than AR, then I might not mind that I hunt or backtrack for the best probabilities overall.

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skydhash 2 days ago | parent | prev [-]

But what about the dependency graph between symbols in the program. Because all those symbols have high constraints around them which is the program design.

The issue comes in image diffusion as well. When you ask it for a portrait and some details are wrong. That’s because the face has constraints (which you learn about as an artist). Patterns and probability won’t help you.

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angusturner 2 days ago | parent [-]

You assume that for small steps (I.e taking some noisy code and slightly denoising) you can make an independence assumption. (All tokens conditionally independent, given the current state).

Once you chain many steps you get a very flexible distribution that can model all the interdependencies.

A stats person could probably provide more nuance, although two interesting connection I’ve seen: There is some sense in which diffusion generalises autoregression, because you don’t have to pick an ordering when you factor the dependency graph.

(Or put otherwise, for some definitions of diffusion you can show autoregression to be a special case).

	▲	skydhash a day ago \| parent [-]
		There’s a reason we have formal verification as the highest guarantee for software. To ensure that we have a complete assurance of what the program can and can not do, the semantic of each of its components needs to be known. Recursively. A minor change in one token can change the meaning of the whole software. Programming is just trying to enforce semantics on instructions (how well is that done is software engineering’s realm) An algorithm like merge sort is just semantic constraints. Which is why most books go with their own notations as code does not really matter. At most, LLMs and diffusion can be regarded as fancy searches. But, what you actually want is semantics and that’s why you can design lots of stuff on paper. But we do it with the code editor because feedbacks are nice and libraries’ documentations (if they exist) lie about their semantics. And we read code because there’s nothing more complete about semantics than that.