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So my personal belief is that diffusion models will enable higher degrees of accuracy. This is because unlike an auto-regressive model it can adjust a whole blo

So my personal belief is that diffusion models will enable higher degrees of accuracy. This is because unlike an auto-regressive model it can adjust a whole block of tokens when it encounters some kind of disjunction. Think of the old example where an auto regressive model would output: "There are 2 possibilities.." before it really enumerated them. Often the model has trouble overcoming the bias and will hallucinate a response to fit the proceeding tokens. Chain of thought and other approaches help overcome this and other issues by incentivizing validation, etc. With diffusion however it is easier for the other generated answer to change that set of tokens to match the actual number of possibilities enumerated. This is why I think you'll see diffusion models be able to do some more advanced problem solving with a smaller number of "thinking" tokens.

AlexCoventry 1y ago
> it can adjust a whole block of tokens when it encounters some kind of disjunction. This is true in principle for general diffusion models, but I don't think it's true for the noise model they use in Mercury (at least, going by a couple of academic papers authored by the Inception co-founders.) Their model generates noise by masking a token, and once it's masked, it stays masked. So the reverse-diffusion gets to decide on the contents of a masked token once, and after that it's fixed.
- macleginn 1y ago
  The exact types of path dependencies in inference on text-diffusion models look like an interesting research project.
  - AlexCoventry 1y ago
    Yes, the problem is coming up with a noise model where reverse diffusion is tractable.
- XenophileJKO 1y ago
  Thank you, I'll have to read the papers. I don't think I have read theirs.
- freeqaz 1y ago
  Here are two papers linked from Inception's site: 1. Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution - https://arxiv.org/abs/2310.16834 https://arxiv.org/abs/2310.16834 2. Simple and Effective Masked Diffusion Language Models - https://arxiv.org/abs/2406.07524 https://arxiv.org/abs/2406.07524
  - AlexCoventry 1y ago
    Thanks, yes, I was thinking specifically of "Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution". They actually consider two noise distributions: one with uniform sampling for each noised token position, and one with a terminal masking (the Q^{uniform} and Q^{absorb}.) However, the terminal-masking system is clearly superior in their benchmarks. https://arxiv.org/pdf/2310.16834#page=6 https://arxiv.org/pdf/2310.16834#page=6
efavdb 1y ago
Suggests an opportunity for hybrids, where the diffusion model might be responsible for large scale structure of response and the next token model for filling in details. Sort of like a multi scale model in dynamics simulations.
fizx 1y ago
Once that auto-regressive model goes deep enough (or uses "reasoning"), it actually has modeled what possibilities exist by the time it's said "There are 2 possibilities.." We're long past that point of model complexity.
- klipt 1y ago
  But as everyone knows, computer science has two hard problems: naming things, cache invalidation, and off by one errors.
pama 1y ago
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.
- niemandhier 1y ago
  This is tremendously interesting! Could you point me to some literature? Especially regarding mathematical proofs of your intuition? I’d like to recalibrate my priors to align better with current research results.
  - pama 1y ago
    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. https://openreview.net/forum?id=tyEyYT267x https://openreview.net/forum?id=tyEyYT267x
  - GistNoesis 1y ago
    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).

AlexCoventry 1y ago

> it can adjust a whole block of tokens when it encounters some kind of disjunction. This is true in principle for general diffusion models, but I don't think it's true for the noise model they use in Mercury (at least, going by a couple of academic papers authored by the Inception co-founders.) Their model generates noise by masking a token, and once it's masked, it stays masked. So the reverse-diffusion gets to decide on the contents of a masked token once, and after that it's fixed.

macleginn 1y ago
The exact types of path dependencies in inference on text-diffusion models look like an interesting research project.
- AlexCoventry 1y ago
  Yes, the problem is coming up with a noise model where reverse diffusion is tractable.
XenophileJKO 1y ago
Thank you, I'll have to read the papers. I don't think I have read theirs.
freeqaz 1y ago
Here are two papers linked from Inception's site: 1. Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution - https://arxiv.org/abs/2310.16834 https://arxiv.org/abs/2310.16834 2. Simple and Effective Masked Diffusion Language Models - https://arxiv.org/abs/2406.07524 https://arxiv.org/abs/2406.07524
- AlexCoventry 1y ago
  Thanks, yes, I was thinking specifically of "Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution". They actually consider two noise distributions: one with uniform sampling for each noised token position, and one with a terminal masking (the Q^{uniform} and Q^{absorb}.) However, the terminal-masking system is clearly superior in their benchmarks. https://arxiv.org/pdf/2310.16834#page=6 https://arxiv.org/pdf/2310.16834#page=6

efavdb 1y ago

Suggests an opportunity for hybrids, where the diffusion model might be responsible for large scale structure of response and the next token model for filling in details. Sort of like a multi scale model in dynamics simulations.

fizx 1y ago

Once that auto-regressive model goes deep enough (or uses "reasoning"), it actually has modeled what possibilities exist by the time it's said "There are 2 possibilities.." We're long past that point of model complexity.

klipt 1y ago
But as everyone knows, computer science has two hard problems: naming things, cache invalidation, and off by one errors.

pama 1y ago

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.

niemandhier 1y ago
This is tremendously interesting! Could you point me to some literature? Especially regarding mathematical proofs of your intuition? I’d like to recalibrate my priors to align better with current research results.
- pama 1y ago
  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. https://openreview.net/forum?id=tyEyYT267x https://openreview.net/forum?id=tyEyYT267x
- GistNoesis 1y ago
  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).