Information Present, Pathway Shut: A Conditional Flow Model That Never Used Its Diffraction Pattern
Abstract
When conditioning fails to improve a conditional generative model, the null is usually read as a limit of the data or the task. We show that it can instead mean the model never used its condition, and we give inexpensive diagnostics that tell the two apart. Our case study is rigid-body flow matching for molecular crystal structure determination from powder X-ray diffraction (PXRD). The pattern enters through zero-initialised, tanh-gated cross-attention. In every trained checkpoint the gate stayed near 5e-5. The pattern changed the predicted velocity by about one part in a million, classifier-free guidance was an identity, and our earlier guided-versus-unguided comparisons had been measuring prior-sampling noise. The gate's gradient was not vanishing. Forcing the gate fully open changed the loss identically for a crystal's own pattern and for another crystal's, because the attention weights behind the closed gate had never learned. An ideal-observer information-ceiling test shows that the pattern resolves 0.05 Å molecular displacements in all 200 held-out crystals tested, even at the lowest training count level. The flat conditioning is therefore a learning failure, not an information limit. We then test, under a pre-registered protocol with a deranged-pattern control, whether fine-tuning with the pathway forced open learns crystal-specific use of the pattern. It does not: even with the pathway open and the information present, the own-pattern advantage is confidently below a small effect (rank-biserial r < 0.15 on every head) and indistinguishable from the deranged-pattern control. That confident null is the full-corpus analysis; on the subset our representation defect provably cannot reach (Sohncke groups, n = 1,116) the pre-registered outcome is instead inconclusive, with the orientation bound at 0.152. We also identify an orientation target that is unlearnable in principle and a rigid-body representation defect that rebuilds improper symmetry copies with the wrong hand and, through a rigidity filter, leaves a corpus in which the two most common organic space groups are under-represented by close to an order of magnitude. We distil the diagnostics into a checklist for conditional generative models in the sciences.
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