Beyond First-Order Tweedie: Solving Inverse Problems using Latent Diffusion

Understand

Sampling from the posterior distribution poses a major computational challenge in solving inverse problems using latent diffusion models.

• Common methods rely on Tweedie's first-order moments, which are known to induce a quality-limiting bias.
• Existing second-order approximations are impractical due to prohibitive computational costs, making standard reverse diffusion processes intractable for posterior sampling.
• This paper introduces Second-order Tweedie sampler from Surrogate Loss (STSL), a novel sampler that offers efficiency comparable to first-order Tweedie with a tractable reverse process using second-order approximation.