Adapt and Diffuse: Sample-Adaptive Reconstruction Via Latent Diffusion Models.

Area of Science:

• Computational mathematics
• Signal processing
• Machine learning

Background:

• Inverse problems are crucial in many applications for recovering signals from degraded observations.
• Reconstruction difficulty varies significantly per sample due to signal structure and degradation.
• Current methods often fail to adapt compute resources to varying reconstruction challenges.

Purpose of the Study:

• To develop a method for estimating reconstruction difficulty on a per-sample basis.
• To create an adaptive inverse problem solver that adjusts computation based on estimated difficulty.
• To accelerate signal recovery in inverse problems without sacrificing accuracy.

Main Methods:

• Severity encoding to estimate signal degradation severity in an autoencoder's latent space.
• Latent diffusion models for signal reconstruction.
• Leveraging predicted degradation severities to fine-tune reverse diffusion sampling trajectories.

Main Results:

• Severity encoding accurately correlates with true corruption levels.
• The proposed method significantly enhances baseline solver performance.
• Achieved up to 10x acceleration in mean sampling speed for inverse problems.

Conclusions:

• Severity encoding provides a robust measure of reconstruction difficulty.
• Sample-adaptive inference using latent diffusion models accelerates inverse problem solving.
• The proposed framework offers a versatile wrapper for enhancing existing solvers.