Rethinking Diffusion Models in Imaging: A Finite-Sample Perspective

Diffusion models have quickly risen to prominence in the imaging field. They're known for their ability to model complex data distributions. Yet, a nagging issue persists, likelihood approximations during sampling frequently lead to unexplained failures.

The Core Issue

At the heart of the problem is the approximation of likelihoods at intermediate timesteps. This shortcut is often necessary for computational feasibility, but its impact on the posterior distribution remains poorly understood. Could these approximations be sabotaging the very accuracy they're meant to enable?

The paper's key contribution: a finite-sample perspective. By considering finite training set sizes, it approximates the posterior with high precision as data volume increases. This approach provides a fresh lens to evaluate how well our models perform.

Why It Matters

Existing methods tend to misjudge the posterior's spread during sampling, leading to inaccurate outcomes. Issues like sensitivity to stopping time and improper weighting of posterior modes emerge. More critically, hallucinations of non-existent prior or likelihood modes occur. Imagine building an elaborate sandcastle on the beach, only to find out it's shifting sand underneath.

Crucially, these errors don't require complex scenarios. A multimodal prior alone, combined with misguided posterior spread, can spark errors. So, can we trust our diffusion models as they stand?

A Diagnostic Approach

What's promising is that this finite-sample approach can serve as a diagnostic tool. It's indifferent to the type of likelihood approximation or forward model used. It evaluates accuracy and identifies failure modes, providing a roadmap for enhancing future samplers.

Incorporating this perspective may be the key to achieving more reliable diffusion models. As datasets grow, understanding this finite-sample reality can drive improvements. Will researchers rise to the challenge of tackling these inaccuracies head-on?