# Steering Optimisation Trajectories in Diffusion Representation Learning

arXiv: https://arxiv.org/abs/2607.05319 · HTML: https://mlsanity.com/paper/2607.05319/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 24 references that are in the map.
- First posted on arXiv 6 Jul 2026.

## Builds on (most cited first, 7 of 7)

- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [Validation, comparison, and combination of algorithms for automatic detection of pulmonary nodules in computed tomography images: the LUNA16 challenge](https://mlsanity.com/paper/1612.08012/) (2016)
- [A roadmap for the computation of persistent homology](https://mlsanity.com/paper/1506.08903/) (2015)
- [PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signatures](https://mlsanity.com/paper/1904.09378/) (2019)
- [Explicit topological priors for deep-learning based image segmentation using persistent homology](https://mlsanity.com/paper/1901.10244/) (2019)
- [The persistence landscape and some of its properties](https://mlsanity.com/paper/1810.04963/) (2018)
- [PI-Net: A Deep Learning Approach to Extract Topological Persistence Images](https://mlsanity.com/paper/1906.01769/) (2019)

## Abstract (arXiv)

We study why diffusion autoencoders can achieve similar image quality while learning substantially different latent structures. We trace this behaviour to optimisation dynamics; we analyse curves of image reconstruction against latent representation quality, revealing trajectories that organise around two distinct regimes early in training. Models in the reconstruction regime prioritise image fidelity early, whereas those in the disentanglement regime improve reconstruction and disentanglement more gradually. We hypothesise that this behaviour can be influenced by targeting shortcut pathways in the diffusion U-Net and controlling early noise-level exposure, thereby shaping the reconstruction-disentanglement trade-off during training. To steer optimisation toward stronger representations, we introduce SteeringDRL, combining gated residual U-Nets with a simple noise-level exposure curriculum for training. Across disentanglement benchmarks, SteeringDRL improves representation quality and reduces seed sensitivity. Our method further extends to spatial disentanglement in object-centric learning, improving segmentation quality on synthetic and real-world datasets.