The Superposition of Diffusion Models Using the Itô Density Estimator
Authors: name: Marta Skreta, name: Lazar Atanackovic, name: Avishek Joey Bose, name: Alexander Tong, name: Kirill Neklyudov

The Cambrian explosion of easily accessible pre-trained diffusion models
suggests a demand for methods that combine multiple different pre-trained
diffusion models without incurring the significant computational burden of
re-training a larger combined model. In this paper, we cast the problem of
combining multiple pre-trained diffusion models at the generation stage under a
novel proposed framework termed superposition. Theoretically, we derive
superposition from rigorous first principles stemming from the celebrated
continuity equation and design two novel algorithms tailor-made for combining
diffusion models in SuperDiff. SuperDiff leverages a new scalable It\^o density
estimator for the log likelihood of the diffusion SDE which incurs no
additional overhead compared to the well-known Hutchinson's estimator needed
for divergence calculations. We demonstrate that SuperDiff is scalable to large
pre-trained diffusion models as superposition is performed solely through
composition during inference, and also enjoys painless implementation as it
combines different pre-trained vector fields through an automated re-weighting
scheme. Notably, we show that SuperDiff is efficient during inference time, and
mimics traditional composition operators such as the logical OR and the logical
AND. We empirically demonstrate the utility of using SuperDiff for generating
more diverse images on CIFAR-10, more faithful prompt conditioned image editing
using Stable Diffusion, and improved unconditional de novo structure design of
proteins. https://github.com/necludov/super-diffusion