Residual Penalties Versus Algebraic Completion In Conditional Diffusion

An exact identity among magnetic-field summaries fixes the redundant sixth coordinate and leaves the conditional law on the five scored coordinates unspecified. We separate that algebraic restriction from the scored distribution by comparing a residual penalty, completion of the redundant sixth coordinate, and support correction after sampling, on one-hour gaps in five-minute NASA OMNI summaries. Completing the sixth coordinate leaves the five energy-score coordinates unchanged, so a residual term can change the score only by changing the first five coordinates. On 480 test windows, validation-selected compatible-residual and data-only diffusion score 1.885 and 1.888, averaged over three fixed training seeds. At the common final update, the compatible penalty lowers all three matched-seed energy scores. Generating the five scored coordinates and deriving the sixth gives the lowest mean energy score. Correcting those same draws barely moves it. Correcting a linear Gaussian can worsen energy score by shrinking ensemble spread. A two-step exact denoiser can have almost zero residual and still miss the conditional distribution. These comparisons use artificial gaps in complete processed records and a historically exposed test period.