UNIVERSITY OF PENNSYLVANIA / MACHINE LEARNING RESEARCH

CASL-VAELearning Structured Latent Variables
from Unpaired Data

for Semi-supervised Clustering and Paired Sample Generation

Sai Spandana ChintapalliPratik Chaudhari†Christos Davatzikos†

Center for AI and Data Science for Integrated Diagnostics (AI2D)

University of Pennsylvania · † Equal advising

Paper (arXiv) View codeCite this work

Discover what is shared.
Understand what makes the target different.

zCommon variationShared across populations
scatSalient subtypesDiscrete target structure
scontWithin-subtype variationContinuous individual differences
01 / OVERVIEW

Learning from contrasts.

How does a heterogeneous target population differ from a reference population when matched samples are unavailable?

CASL-VAE separates common variation from target-specific variation using a hierarchical salient latent space: a discrete variable captures subtypes, and a conditional continuous variable captures differences within each subtype. This structure supports subtype discovery and paired sample generation from unpaired observations.

Training uses reference/target labels. No target subtype labels or matched pairs are required.

02 / METHOD

One model. Three latent factors.

Separate shared variation.
Structure the salient differences.

CASL-VAE architecture: shared common and salient encoders and additive decoders trained on unpaired target and reference samples. Inference supports paired reference generation, subtype inference, and salient variation.
FIG. 1 Unpaired training and downstream applications. Reference samples use a preset salient category and zero continuous salient code.
A

Encode the common

The common latent z captures variation shared across reference and target populations.

B

Structure the salient

A categorical latent captures subtype structure. A conditional continuous latent captures variation within each subtype.

C

Generate a counterpart

Keep z fixed and decode with the reference salient preset to estimate a paired reference sample.

EXPLORE THE MODEL OUTPUTS

x → q(scat | x) → subtype

Discover target structure without subtype labels.

Infer category probabilities from the salient encoder. One category is reserved for the reference population; the remaining categories represent target subtypes.

03 / RESULTS

From latent factors to interpretable patterns.

Semi-synthetic neuroimaging experiments provide known atrophy patterns and severity for evaluating the learned representation.

Three learned subtype patterns in red and blue, above their corresponding ground-truth yellow brain-region masks.
FIG. 2 Learned subtype prototypes (top) and ground-truth masks (bottom), with 10–30% simulated atrophy. Red indicates lower volume relative to reference; yellow marks simulated regions.

BEYOND A CLUSTER LABEL

Different subtypes.
Continuous differences.

The hierarchical salient space captures both category membership and variation within each category. Here, continuous posterior means are colored by the ground-truth simulated atrophy rate.

Reference samples remain near the preset origin, while target samples exhibit within-subtype structure.

Four panels of continuous salient posterior means for reference and three target subtypes, colored by simulated atrophy rate.
FIG. 3 Conditional continuous salient representations on held-out samples.

Quantitative evaluation

Semi-synthetic neuroimaging · mean across 10 repeated splits

CASL-VAE performance in the paper's semi-synthetic neuroimaging experiments
CASL-VAE metricMild atrophy 10–20%Typical atrophy 10–30%
Target-only clustering ARI ↑0.468 (0.371, 0.564)0.620 (0.535, 0.706)
Target + reference clustering ARI ↑0.587 (0.521, 0.653)0.697 (0.672, 0.722)
Paired reference generation Cosine similarity ↑0.5835 (0.5777, 0.5894)0.5816 (0.5747, 0.5885)

Parentheses show 95% confidence intervals. Values from Tables 1–2 of the paper; see the paper for baselines and statistical comparisons.

Two prototypical target patterns learned in ADNI MCI and AD participants relative to cognitively normal participants.
FIG. 4 ADNI target patterns relative to the cognitively normal reference population.

04 / REAL-WORLD APPLICATION

Characterizing heterogeneity in Alzheimer's disease.

In ADNI, stability-based category selection yields two target patterns with different regional distributions of volume loss. Individual deviation estimates are associated with clinical and biomarker measures.

These learned categories may reflect subtype, severity, or overlapping mechanisms. Biological interpretation requires independent validation.

Explore the experiments in the paper

05 / GET STARTED

Bring your own
reference–target data.

Explore the implementation, prepare feature measurements, and train CASL-VAE on your populations.

IMPLEMENTATIONCode & installationPRACTICAL GUIDETraining & inference examplesARXIV PREPRINTMethod, experiments & appendix

06 / CITATION

Build on this work.

@misc{chintapalli2026casl,
  title={CASL-VAE: Learning Structured Latent Variables from Unpaired Data
         for Semi-supervised Clustering and Paired Sample Generation},
  author={Chintapalli, Sai Spandana and Chaudhari, Pratik
          and Davatzikos, Christos},
  year={2026},
  eprint={2607.08254},
  archivePrefix={arXiv},
  url={https://arxiv.org/abs/2607.08254}
}