Estimating Probability Densities with Transformer and Denoising Diffusion
This provides a flexible density function emulator for scientific applications where full probabilistic outputs are crucial, though it appears incremental as it adapts existing methods.
The authors tackled the problem of probability density estimation for high-dimensional, non-Gaussian data in scientific fields by combining a Transformer with a denoising diffusion head, enabling accurate inference with reasonable distributions on astronomical data.
Transformers are often the go-to architecture to build foundation models that ingest a large amount of training data. But these models do not estimate the probability density distribution when trained on regression problems, yet obtaining full probabilistic outputs is crucial to many fields of science, where the probability distribution of the answer can be non-Gaussian and multimodal. In this work, we demonstrate that training a probabilistic model using a denoising diffusion head on top of the Transformer provides reasonable probability density estimation even for high-dimensional inputs. The combined Transformer+Denoising Diffusion model allows conditioning the output probability density on arbitrary combinations of inputs and it is thus a highly flexible density function emulator of all possible input/output combinations. We illustrate our Transformer+Denoising Diffusion model by training it on a large dataset of astronomical observations and measured labels of stars within our Galaxy and we apply it to a variety of inference tasks to show that the model can infer labels accurately with reasonable distributions.