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A diffusion model learns to predict a vector field of gradients. We proposeto apply chain rule on the learned gradients, and back-propagate the score of adiffusion model through the Jacobian of a differentiable renderer, which weinstantiate to be a voxel radiance field. This setup aggregates 2D scores atmultiple camera viewpoints into a 3D score, and repurposes a pretrained 2Dmodel for 3D data generation. We identify a technical challenge of distributionmismatch that arises in this application, and propose a novel estimationmechanism to resolve it. We run our algorithm on several off-the-shelfdiffusion image generative models, including the recently released StableDiffusion trained on the large-scale LAION dataset.

Score Jacobian Chaining: Lifting Pretrained 2D Diffusion Models for 3D Generation