Diffusion with Forward Models: Solving Stochastic Inverse Problems Without Direct Supervision

TL;DR

This paper introduces a novel diffusion model framework that learns to generate signals from indirect measurements via a known forward model, enabling applications like 3D scene generation from 2D images without direct supervision.

Contribution

The authors propose integrating a differentiable forward model into diffusion processes, allowing end-to-end training for inverse problems with indirect observations.

Findings

Effective in inverse graphics for 3D scene sampling from 2D images

Enables end-to-end training with indirect measurements

Demonstrates success on three challenging computer vision tasks

Abstract

Denoising diffusion models are a powerful type of generative models used to capture complex distributions of real-world signals. However, their applicability is limited to scenarios where training samples are readily available, which is not always the case in real-world applications. For example, in inverse graphics, the goal is to generate samples from a distribution of 3D scenes that align with a given image, but ground-truth 3D scenes are unavailable and only 2D images are accessible. To address this limitation, we propose a novel class of denoising diffusion probabilistic models that learn to sample from distributions of signals that are never directly observed. Instead, these signals are measured indirectly through a known differentiable forward model, which produces partial observations of the unknown signal. Our approach involves integrating the forward model directly into the denoising process. This integration effectively connects the generative modeling of observations with the generative modeling of the underlying signals, allowing for end-to-end training of a conditional generative model over signals. During inference, our approach enables sampling from the distribution of underlying signals that are consistent with a given partial observation. We demonstrate the effectiveness of our method on three challenging computer vision tasks. For instance, in the context of inverse graphics, our model enables direct sampling from the distribution of 3D scenes that align with a single 2D input image.