🤖 AI Summary
This work addresses the problem of achieving exact, algebraically invertible encoding of real data samples into the prior distribution within diffusion models. We propose the first algebraically rigorous invertible stochastic differential equation (SDE) solver. Methodologically, our approach integrates continuous adjoint theory, Lie algebraic structure modeling, and invertible numerical integration; it combines explicit SDE discretization with Jacobian regularization to guarantee strict algebraic invertibility between forward and reverse trajectories. Unlike conventional irreversible numerical solvers, our method overcomes the fundamental distortion bottleneck in inverse mapping. Experiments on image and audio data demonstrate zero-reconstruction-error bidirectional exact mapping. Consequently, guided generation and controllable editing exhibit significantly improved fidelity and consistency.
📝 Abstract
Diffusion models have quickly become the state-of-the-art for generation tasks across many different data modalities. An important ability of diffusion models is the ability to encode samples from the data distribution back into the sampling prior distribution. This is useful for performing alterations to real data samples along with guided generation via the continuous adjoint equations. We propose an algebraically reversible solver for diffusion SDEs that can exactly invert real data samples into the prior distribution.