# Controlla: Learning Controllability via Graph-Constrained Latent Geometry

arXiv: https://arxiv.org/abs/2605.16603 · HTML: https://mlsanity.com/paper/2605.16603/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 64 references that are in the map.
- First posted on arXiv 15 May 2026.

## Builds on (most cited first, 23 of 23)

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## Abstract (arXiv)

Controllable multimodal generation is commonly formulated as an inference-time conditioning problem using prompts, guidance, or auxiliary modules. While effective, such approaches do not explicitly structure how semantic attributes evolve, which can lead to identity drift and inconsistent cross-modal behavior. We propose Controlla, a modular factorized-control framework that treats controllability as a property of structured latent geometry. Controlla learns identity and attribute factors from multimodal inputs and aligns them with graph priors using graph-constrained optimal transport, encouraging attributes to follow graph-consistent trajectories while preserving reference identity. To evaluate this setting, we construct AffectHuman-43K, a leakage-aware multimodal benchmark for reference-grounded affective control, and introduce geometry-aware metrics for trajectory consistency and latent disentanglement. Experiments show consistent improvements in controllability, identity preservation, and cross-modal alignment, with additional analyses on graph sensitivity, extensibility, and robustness.