Score Accuracy Along the Forward Diffusion Does Not Certify Numerical Stability in Diffusion Sampling
When AI image generators seem accurate but actually produce unstable results
Diffusion models—the AI systems behind image generators—are usually trained to match real data distributions accurately, but this training goal doesn't guarantee the sampling process will remain numerically stable. Researchers constructed examples where a learned score function has negligibly small error by standard measures, yet its discretized sampling algorithm produces outputs with wildly diverging statistical properties, contradicting what the training metrics predicted.
Diffusion models power real products like DALL-E and Stable Diffusion. If a model passes standard accuracy tests but fails on numerical stability, it could generate bizarre or corrupted images on rare trajectories—failures that wouldn't be caught by conventional evaluation. The researchers also show that constraining the learned function to stay within known bounds fixes the problem, offering a practical safeguard for production systems.