[nvtop]

Despite the name, diffusion LMs have little to do with image diffusion and are much closer to BERT and old good masked language modeling. Recall how BERT is trained:

1. Take a full sentence ("the cat sat on the mat") 2. Replace 15% of tokens with a [MASK] token ("the cat [MASK] on [MASK] mat") 3. Make the Transformer predict tokens at masked positions. It does it in parallel, via a single inference step.

Now, diffusion LMs take this idea further. BERT can recover 15% of masked tokens ("noise"), but why stop here. Let's train a model to recover texts with 30%, 50%, 90%, 100% of masked tokens.

Once you've trained that, in order to generate something from scratch, you start by feeding the model all [MASK]s. It will generate you mostly gibberish, but you can take some tokens (let's say, 10%) at random positions and assume that these tokens are generated ("final"). Next, you run another iteration of inference, this time input having 90% of masks and 10% of "final" tokens. Again, you mark 10% of new tokens as final. Continue, and in 10 steps you'll have generated a whole sequence. This is a core idea behind diffusion language models.

Of course, there are some optimizations in the real world. If you need to generate a really long text (over 200 tokens), you'd better split it in chunks and fully generate the first chunk in parallel before moving to the next one. This semi-autoregressive generation is what Block Diffusion does.

You can be smart about how exactly you pick tokens you consider generated and what % exactly. At earlier stages, when it's mostly noise, you can take more, and on final stages you can do more iterations and take fewer tokens.

All in all, diffusion LMs are still iterative, but the number of steps is much lower than in autoregressive models. A nice thing is that you can choose how many steps are you going to make, trading quality for speed.

In the extreme, you can even generate just one leftmost masked token with a diffusion LM, effectively turning it into a traditional causal language model.

[yahoozoo]

Great explanation. I think I have seen where text diffusion models can “edit” as it’s running inference. Or in other words, a “final” token isn’t necessarily “final” and could change but at some later iteration the model decides it truly is. How does that work?

[nvtop]

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.

[paulsmith]

> 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.

[skydhash]

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.

[angusturner]

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]

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.

[oliwary]

Fascinating, and great explanation.

What about insert and delete operations however? Isn't there a risk of there being too few tokens to properly finish the code in-between the "final" tokens?

[Workaccount2]

Can you have a hybrid model that can do autoregression and diffusion? It doesn't seem like there is something that would fundamentally prevent this. A model with diffusion CoT for rapid "thought" generation, and then autoregression for the answer on the output.

[nvtop]

You can absolutely do it, and I think it's a nice idea to try.

[shawntan]

I'm curious how the speed is achieved is this is the technique used. Generally I expected this "masked language model" technique to be far slower since the full vocab projection needs to be computed every iteration.

I always thought the eventual technique would be some form of diffusion in continuous space, then decoding into the discrete tokens.

Also I'm guessing this is a "best guess" of how Gemini Diffusion is done?

[victorbjorklund]

Thanks. Best explanation of text diffusion.

[moralestapia]

Whoa man, thanks.

This is a great explanation.

[ctxc]

Thank you for the explanation!