A single brain scan can still place a patient on the disease timeline: ELPAC anchors on clinical endpoints and integrates backward

ELPAC inverts the direction of supervision: instead of growing trajectories forward from the earliest, least certain subjects, it starts from clinically confirmed endpoint groups and integrates backward along each modality's monotone direction of change to place every subject on a continuous stage. Earlier disease-progression models grew trajectories forward from the cohort's most uncertain early and intermediate subjects, or estimated subtype-specific mean trajectories without the multivariate dependence around them. On synthetic cohorts, removing endpoint anchoring lowers subtype balanced accuracy and worsens cognition alignment, while stage Spearman correlation against ground truth stays within a few percentage points of the full model, indicating that boundary supervision carries the subtype signal and orients the stage axis.

Around that stage axis, residual multimodal variation is split into sparse coordination axes, each naming which regions and modalities co-vary and when along progression that co-variation emerges or fades. Condition-varying covariance models treat the condition as observed, whereas here the stage itself is latent; multimodal fusion networks read the data through a predictive lens rather than a progression-resolved one. On the harmonized ADNI+NACC/SCAN cohort, replacing the coordination axes with a static-factor covariance lowers subtype balanced accuracy, and a diagonal covariance widens the held-out and masked negative log-likelihood gaps by about the same amount each, while the full model leads held-out likelihood, subtype recovery, both diagnostic AUCs and masked reconstruction.

Inference uses an amortized variational scheme with structured low-rank updates to global parameters, so a new subject needs a single encoder forward pass to obtain a posterior over subtype, stage and trajectory. Joint posterior inference had been hard to scale to cohort size, and the amortized scheme makes the global-parameter cost grow linearly with cohort size. On the harmonized ADNI+NACC/SCAN cohort, the full model fits on a single GPU faster than SuStaIn and HEALNet and returns posteriors over subtype, stage, trajectories and stage-varying coordination together.

The demonstrated scope is synthetic cohorts and a harmonized cross-sectional Alzheimer's cohort pooled from ADNI and NACC with SCAN-standardized imaging, retaining subjects whenever any of four modalities (amyloid PET, tau PET, structural MRI, plasma biomarkers) is observed, with performance evaluated over 20 random anchor-stratified train-test splits. The intended reader is a researcher who must infer progression and multimodal coordination from partially observed cross-sectional data; the recovered stage axis is pseudo-temporal, and the coordination factors describe co-variation along it rather than mechanism.

The stage axis is pseudo-temporal, recovered from cross-sectional snapshots, so coordination factors describe co-variation along it rather than mechanism; the dependency layer models only second-order multimodal coordination, with higher-order joint dependence left as future work; the full-model identifiability proposition invokes a Gaussian mixing-family hypothesis, and Theorem 1 identifies the dynamic factor block only conditionally; amortized variational inference approximates the true posterior. Under anchor corruption, subtype and stage recovery degrade smoothly with label noise: at 20% uniform mislabeling, synthetic subtype accuracy and stage correlation fall by 3.4 and 5.7 percentage points and real-cohort balanced accuracy by 7.0 percentage points.