Simone Scardapane Profile picture
Jun 16, 2021 13 tweets 12 min read Read on X
*Score-based diffusion models*

An emerging approach in generative modelling that is gathering more and more attention.

If you are interested, I collected some introductive material and thoughts in a small thread. 👇

Feel free to weigh in with additional material!

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An amazing property of diffusion models is simplicity.

You define a probabilistic chain that gradually "noise" the input image until only white noise remains.

Then, generation is done by learning to reverse this chain. In many cases, the two directions have similar form.

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The starting point for diffusion models is probably "Deep Unsupervised Learning using Nonequilibrium Thermodynamics" by @jaschasd Weiss @niru_m @SuryaGanguli

Classic paper, definitely worth reading: arxiv.org/abs/1503.03585

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A cornerstone in diffusion models is the introduction of "denoising" versions by @hojonathanho @ajayj_ @pabbeel

They showed how to make diffusion models perform close to the state-of-the-art using a suitable reformulation of their training objective.

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It turns out that the improved version is also simpler than the original one!

Roughly, it works by adding noise to an image, and learning to denoise the image itself.

In this way, training is connected to denoising autoencoders, and sampling remains incredibly easy.

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Denoising diffusion turns out to be similar to "score-based" models, pioneered by @YSongStanford and @StefanoErmon

@YSongStanford has written an outstanding blog post on these ideas, so I'll just skim some of the most interesting connections: yang-song.github.io/blog/2021/scor…

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Score-based models work by learning an estimator for the score function of the distribution (ie, the gradient of the log).

Langevin dynamics allows to sample from p(x) having only access to the estimator of the score function.

Reference paper here: arxiv.org/abs/1907.05600

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Naive score-based models are uncommon, because sampling starts in poorly approximated regions.

The solution is noise-conditional score models, that perturb the original input, and generate data using "annealed" Langevin dynamics.

arxiv.org/abs/2006.09011
Noise-conditional score-based models and denoised diffusion models are almost equivalent, basically a single family of models.

A few additional improvements obtain performance close to BigGAN on complex datasets, as shown by @prafdhar @unixpickle

arxiv.org/abs/2105.05233

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Interestingly, when the noise variance goes from discrete values to a continuous distribution, score-based models connect to neural SDEs and continuous normalizing flows!

This was shown in a #ICLR2021 paper by @YSongStanford @jaschasd @dpkingma Kumar @StefanoErmon @poolio

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The field is exploding, too many interesting papers to cite!

For example, a recent one by @YSongStanford @conormdurkan @driainmurray @StefanoErmon shows that a formulation of score-based models is upper-bounding a maximum likelihood objective.

arxiv.org/pdf/2101.09258…

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Another personal favorite: multinomial diffusion and argmax flows extend score-based models and flows to discrete data distributions!

by @emiel_hoogeboom @nielsen_didrik @priyankjaini
Forré @wellingmax

arxiv.org/abs/2102.05379

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I could go on with my new love, but I'll stop. 🙃

Another nice blog post on score-based models: ajolicoeur.wordpress.com/the-new-conten…

Introductive video by @StefanoErmon:

Lots of code in the blog post by @YSongStanford!

Or you can play w/ github.com/lucidrains/den…

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More from @s_scardapane

Sep 20, 2022
Gather round, Twitter folks, it's time for our beloved
**Alice's adventures in a differentiable wonderland**, our magical tour of autodiff and backpropagation. 🔥

Slides below 1/n 👇 Image
It all started from her belief that "very few things indeed were really impossible". Could AI truly be below the corner? Could differentiability be the only ingredient that was needed?

2/n Image
Wondering were to start, Alice discovered a paper by pioneer @ylecun promising "a path towards autonomous intelligent agents".

Intelligence would arise, it was argued, by several interacting modules, were everything was assumed to be *differentiable*.

3/n Image
Read 17 tweets
Mar 10, 2022
*Generative Flow Networks*

A new method to sample structured objects (eg, graphs, sets) with a formulation inspired to the state space of reinforcement learning.

I have collected a few key ideas and pointers below if you are interested. 👀

1/n

👇 Image
*Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation*
#NeurIPS paper by @folinoid @JainMoksh et al. introducing the method.

The task is learning to sample objects that can be built 1 piece at a time ("lego-style").

2/n

arxiv.org/abs/2106.04399 Image
For example: a complex molecule can be built by adding one atom at a time; an image by colouring one pixel per iteration; etc.

If you formalize this process, you get a state space where you move from an "empty" object to a complete object by traversing a graph.

3/n Image
Read 13 tweets
Dec 28, 2021
*Neural networks for data science* lecture 8 is out!

And it's already the last lecture! 🙀

What lies beyond classical supervised learning? It turns out, _way_ too many subfields!

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Here is my overview of everything that can happen when we have > 1 "task": fine-tuning, pre-training, meta learning, continual learning...

The slides have my personal selection of material. 😎

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The slides are here: sscardapane.it/assets/files/n…

All the material, as always, is here: sscardapane.it/teaching/nnds-…

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Read 4 tweets
Nov 3, 2021
*Neural networks for data science* lecture 4 is out! 👇

aka "here I am talking about convolutional neural networks while everyone asks me about transformers"

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CNNs are a great way to show how considerations about the data can guide the design of the model.

For example, only assuming locality (and not transl. invariance) we get locally-connected networks.

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Everything else is a pretty standard derivation of CNN ideas (stride, global pooling, receptive field, ...).

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Read 7 tweets
Aug 2, 2021
*Reproducible deep learning*: Time for exams!

To a practical course, a practical exam: I asked each student to include a new branch in the repository showcasing additional tools and libraries.

The result? *Everyone* loves some hyper-parameter optimization. 😄

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Thanks to their work, you'll find practical examples of fine-tuning parameters using @OptunaAutoML, AX (from @facebookai), @raydistributed Tune, and Auto-PyTorch and Talos coming soon.

So many ideas for next year! 😛

github.com/sscardapane/re…

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You will also find additional exercises on:

- Serving the model with TorchServe;
- Managing experiments with @DVCorg 2.0;
- Set up cron jobs for re-training.

BTW, if you'd like to add something, feel free to contact me or open a pull request. 🙂

github.com/sscardapane/re…

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Read 4 tweets
Jun 14, 2021
*LocoProp: Enhancing BackProp via Local Loss Optimization*
by @esiamid @_arohan_ & Warmuth

Interesting approach to bridge the gap between first-order, second-order, and "local" optimization approaches. 👇

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The key idea is to use a single GD step to define auxiliary local targets for each layer, either at the level of pre- or post-activations.

Then, optimization is done by solving local "matching" problems wrt these new variables.

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What is intriguing is that the framework interpolates between multiple scenarios: first solution step is the original GD, while closed-form solution (in one case) is similar to a pre-conditioned GD model. Optimization is "local" in the sense that it decouples across layers.

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Read 4 tweets

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