Crystal diffusion model reaches property targets more often when it also generates Bader charges

The problem the authors set out to fix is that conditioning a generator on a property can erode the structural quality it otherwise achieves ^[10]. Their account of why joint denoising helps is that the descriptors guide the structural trajectory toward electronically plausible configurations, and that they widen the explored materials space through greater structural diversity ^[11]. The experiments test something narrower than that interpretation.

The controls carry most of the evidential weight. The authors ran one with noise-corrupted Bader charges and one with a physically uninformative dummy variable, and report that the gains require the jointly generated variable to reflect the true local electronic structure ^[6]. In our reading, that rules out the cheapest explanation: that any extra output channel in the score network helps through added capacity or regularisation. It does not by itself prove the trajectory-guiding story in ^[11].

The Bader charge error of 5.4 x 10^-2 e is computed on structures already filtered for stability, uniqueness and novelty ^[7], so it describes the generator's best output, not every sample. The atomic DOS is looser. At the median of its accuracy distribution, the generated DOS gets the broad shape of the DFT reference spectrum right, and finer detail and accuracy vary with the element ^[8]. At the median, half of the generated structures are less accurate than that, by definition ^[9].

The material supplied does not include the success rates, the number of structures sampled per target, how success was judged for band gap and formation energy, or what the extra variables cost at sampling time. Success rate against a target is a research leaderboard number. A production number would count DFT-confirmed hits per unit of compute, and the baseline comparison could look different on that scale.