Akhil Premkumar

Akhil Premkumar, Sarah Lucioni

We construct a new kind of encoder, leveraging the expressive power of diffusion models. In a traditional variational autoencoder, the encoder and decoder jointly negotiate a latent representation of the input. This is made possible by the reparameterization trick, which simplifies training at the cost of restricting the encoder to a simple family of distributions. Replacing this encoder with a diffusion model requires rethinking how the decoder pressure can be transmitted back to the encoder, given that they tend to update their internal estimates of the latent in opposing directions. We solve this problem with an alternating training scheme, inspired by the expectation-maximization algorithm. Our method enables more reliable synchronization between encoder and decoder, while preserving the simple and efficient training objective of standard diffusion models.

Akhil Premkumar

We explore the connection between deep learning and information theory through the paradigm of diffusion models. A diffusion model converts noise into structured data by reinstating, imperfectly, information that is erased when data was diffused to noise. This information is stored in a neural network during training. We quantify this information by introducing a measure called neural entropy, which is related to the total entropy produced by diffusion. Neural entropy is a function of not just the data distribution, but also the diffusive process itself. Measurements of neural entropy on a few simple image diffusion models reveal that they are extremely efficient at compressing large ensembles of structured data.

Akhil Premkumar

Generative diffusion models synthesize new samples by reversing a diffusive process that converts a given data set to generic noise. This is accomplished by training a neural network to match the gradient of the log of the probability distribution of a given data set, also called the score. By casting reverse diffusion as an optimal control problem, we show that score matching can be derived from an action principle, like the ones commonly used in physics. We use this insight to demonstrate the connection between different classes of diffusion models.

Akhil Premkumar

We draw a connection between diffusion models and the Kelly criterion for maximizing returns in betting games. We find that conditional diffusion models store additional information to bind the signal $X$ with the conditioning information $Y$, equal to the mutual information between them. Classifier-free guidance effectively boosts the mutual information between $X$ and $Y$ at sampling time. This is especially helpful in image models, since the mutual information between images and their labels is low, a fact which is intimately connected to the manifold hypothesis. Finally, we point out some nuances in the popular perspective that diffusion models are infinitely deep autoencoders. In doing so, we relate the denoising loss to the Fermi Golden Rule from quantum mechanics.