Explorative modeling: Train on the best of K guesses
alexiglad.github.io
alexiglad.github.io
They repeatedly claim that previous approaches rely on factorization to reduce things to guessable chunks to avoid the 'blur problem'. This is a misunderstanding. Previous approaches solve this problem by modelling a distribution as output rather than a point. Factorization is one way of representing the distribution, but the key point is that even for the small chunks we predict an output distribution, not a point estimate.
Factored models have no issue producing TV static as an image. Each individual guess is impossible, and yet they don't produce a constant grey averaged image.
Normalizing flows, though not considered particularly efficient, are not factored at all, do not proceed in small steps, and yet still have no issues with blur because they predict a distribution.
Their approach appears to be a hard version of a latent variable model. It may be a good idea, but it isn't a fundamental change in the way they suggest.
1. K-1 extra forward passes during training
2. Inaccurate sampling behavior (will sample all K modes with equal likelihood, rather than sampling them proportionally)
However, I think both of these downsides can be mitigated by adjusting the implementation a bit more (you can have the model predict K modes jointly in one forward pass, along with probabilities of each being the min-loss mode, which you can then use for properly-weighted mode sampling at inference).
That said, I'm not entirely sure if this strategy is as generally applicable as the authors are hoping. In particular:
1. For highly-conditional image generation (like modern commercial diffusion pipelines, which use a big LLM preprocessor), most of the low-frequency color/layout decisions are already made for you by the conditioning signal. The diffusion process mostly needs to generate high-frequency details, for which there are a huge number of equally-valid modes.
2. For LLMs themselves, the sequence-generation process is already factored into a discrete classification problem, and there's no mode smearing issue to fix.
I was just reading this great breakdown of how diffusion Gemma works: https://newsletter.maartengrootendorst.com/p/a-visual-guide-...
In reference to the difficulties with applying this to autoregressive LLMs - I wonder if these type of hybrids might be a good candidate for this approach.
Also, a very well-structured and easy to follow blog post by the author. I very much enjoyed reading it!
IWAE: sample a bunch of latents, weight the loss of training the model using each one by softmax(-error). For images and text where the errors have large variance, those weights become one-hot, yielding this algorithm.
Paper: https://arxiv.org/abs/2401.00036 Project page: https://discrete-distribution-networks.github.io/
Given that these were published at ICML 2025, at which the author was a top reviewer as per their own website https://alexiglad.github.io/, I wonder how influenced they were to pursue this avenue of the back of it. They do have a related works section in appendix E, but it somehow seems to miss this. Which is odd, as the paper made a splash at the time at the conference and even made it close to the top of hacker news due to the novelty.
Of course, DDNs are a fundamentally new architecture, whereas this is more a generaliseable training strategy, but there is a very similar core.
Factoring is something we do to distributions, which we then parameterize with our neural net.
An autoregressive model pertains to a certain factorisation of a joint distribution. And if we choose this factorisation it may have consequences for our training and sampling etc.
But to say "most models on factor generation".. I dont quite get this.
This would be better work if it didnt claim it was a new pretraining axis also. Its another way of scaling compute right?
If it were a new axis, IWAE would have an equal claim to it (as others have pointed out).
Minibatch OT in flow matching also has a very similar mechanism, where samples from a noise distribution are matched to the closest data point.
There is a lot of prior work here that the authors neglect to discuss, which portrays this work as more novel than it actually is.
A comparison with minibatch optimal transport is in appendix A.2 of the paper.
GRPO (or GRPO like approaches) for diffusion/flow matching similarly can be likelihood free.
Do you have a particular paper in mind that does likelihood-free best-of-K but just calls it GRPO?
Likelihood is not fundamental to the spirit of GRPO, any exploratory mechanism would work.
That sequential LLMs have a step-wise probability is convenient but not critical to this approach (where rejection sampling is widely used in diffusion models).
Exploration beyond Pretraining. The mode collapse XMs address during pretraining also often shows up in post-training, where RL fine-tuning is known to sharpen models onto a narrow set of behaviors [76]. Recent fixes such as pass@krewards [77] and best-of-N-aware fine-tuning [78] can be seen through our lens as Forward XM, with a verifier standing in for ground truth data. These fixes act only during post-training, though; pretraining with exploration may yield base models that capture more modes in the first place, leaving RL more to select among.
On the other hand, Minibatch OT (optimal transport) was one of the more fundamental advancements early on in flow matching & rectified flow models.
This best of K approach effectively discards matches that would otherwise be preserved by optimal transport assignment.
I still think the authors here are too broad regarding their claimed novelty.