Hidden non-conservativity in structure prediction models

Increasingly, macromolecular structure prediction models using diffusion architectures are used not just to predict static structures but to generate conformational ensembles, inviting interpretations in terms of state probabilities or free-energy landscapes. We test a simple prerequisite for this scientific-discovery interpretation: whether the learned coordinate denoising field is locally integrable. The whole score Jacobian appears nearly symmetric, but in reality is dominated by the symmetric diffusion self-term. Isolating the inter-residue (i.e. off-diagonal) portion reveals widespread non-reciprocity: at $\sigma = 4$ Å, median $\lambda_{\mathrm{off}}$ is 0.195 in Boltz-2 and 0.098 in ESMFold2-Fast, with weak cross-model correlation ($r = 0.2759$). In both models, non-reciprocity correlates with low confidence (Boltz-2: mean pLDDT versus $\lambda_{\mathrm{off}}$: Spearman $\rho = -0.3868$; ESMFold2-Fast: Spearman $\rho = -0.3193$) but remains substantial even in high confidence proteins. MSA conditioning reduces local non-reciprocity, while path dependence is essentially unchanged. Finally, across $n = 25$ experimentally characterized two-state proteins, we demonstrate path-dependence with a standardized $1$ Å direct-versus-detour analysis between conformational endpoints, with median multiplicative disagreements of 2.24 in Boltz-2 and 2.98 in ESMFold2-Fast. These results falsify the scalar-landscape interpretation for the implemented Cartesian denoising fields: they do not in general define a unique scalar conformational landscape, an effect obscured by the dominance of the symmetric self-term.