Breaking Observable Degeneracy in Diffusion Models of Amorphous Matter

Diversity in conditional samples from a generative model can reflect either creativity or hallucination. In the physical sciences, this ambiguity is critical when inverting an experimental measurement, since choosing among the solutions requires an intractable ground truth that the generative model is meant to replace. Using disordered materials as a challenging case study, we show that a score-based denoiser systematically produces samples of high configurational entropy that the conditional input cannot distinguish from the reference. This amounts to a residual excess temperature, raising the concentration of outliers in the system and compromising the physical behavior of the samples. To break this degeneracy, we implement four modifications to the sampling routine that suppress this residual noise: a gate interpolating between the reverse SDE and the probability-flow ODE; guidance on the low-frequency bands that the experimental observable leaves undetermined; a structural relaxation projected onto the null space of the observable's Jacobian; and a ladder of partial restarts. Together, these measures halve the excess entropy on benchmark systems and allow reaching amorphous configurations that quench kinetics have kept out of reach of direct simulation for decades.