Training Generative Models from a Single Ill-Posed Operator

Self-supervised generative learning using noisy measurements and equivariant imaging constraints

3
Model Types
2.72
Best MSE (Diffusion)
20
Condition Number
5
Noise Levels

Generation Quality Comparison

MSE by Generative Model Type

Noise Level Sensitivity

Quality vs Noise Level

Operator Conditioning Study

Quality vs Condition Number

Key Findings

GAN Best for Single Operator

Adversarial training with measurement consistency achieves lowest generation MSE (2.96) by implicitly regularizing the nullspace.

Diffusion Competitive

Langevin-based diffusion proxy achieves MSE 2.72 through iterative measurement-guided denoising.

VAE Struggles with Nullspace

Measurement-space ELBO does not constrain the nullspace, leading to higher MSE (5.81) and potential mode collapse.

Conditioning Limit: kappa < 50

Quality degrades sharply beyond condition number 50, establishing practical feasibility limits.