# Multi-view diffusion geometry using intertwined diffusion trajectories

arXiv: https://arxiv.org/abs/2512.01484 · HTML: https://mlsanity.com/paper/2512.01484/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 43 references that are in the map.
- First posted on arXiv 1 Dec 2025.

## Builds on (most cited first, 12 of 12)

- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [PageRank beyond the Web](https://mlsanity.com/paper/1407.5107/) (2014)
- [BayesOpt: A Bayesian Optimization Library for Nonlinear Optimization, Experimental Design and Bandits](https://mlsanity.com/paper/1405.7430/) (2014)
- [Latent common manifold learning with alternating diffusion: analysis and applications](https://mlsanity.com/paper/1602.00078/) (2016)
- [Are Cluster Validity Measures (In)valid?](https://mlsanity.com/paper/2208.01261/) (2022)
- [Recovering Hidden Components in Multimodal Data with Composite Diffusion Operators](https://mlsanity.com/paper/1808.07312/) (2018)
- [Convolutional Learning on Multigraphs](https://mlsanity.com/paper/2209.11354/) (2022)
- [Multimodal Data Visualization and Denoising with Integrated Diffusion](https://mlsanity.com/paper/2102.06757/) (2021)
- [Het-node2vec: second order random walk sampling for heterogeneous multigraphs embedding](https://mlsanity.com/paper/2101.01425/) (2021)
- [Generalized Dirichlet Energy and Graph Laplacians for Clustering Directed and Undirected Graphs](https://mlsanity.com/paper/2203.03221/) (2022)
- [Stein Boltzmann Sampling: A Variational Approach for Global Optimization](https://mlsanity.com/paper/2402.04689/) (2024)
- [Parametrized Power-Iteration Clustering for Directed Graphs](https://mlsanity.com/paper/2210.00310/) (2022)

## Abstract (arXiv)

This paper introduces a comprehensive unified framework for constructing multi-view diffusion geometries through intertwined multi-view diffusion trajectories (MDTs), a class of inhomogeneous diffusion processes that iteratively combine the random walk operators of multiple data views. Each MDT defines a trajectory-dependent diffusion operator with a clear probabilistic and geometric interpretation, capturing over time the interplay between data views. Our formulation encompasses existing multi-view diffusion models, while providing new degrees of freedom for view interaction and fusion. We establish theoretical properties under mild assumptions, including ergodicity of both the point-wise operator and the process in itself. We also derive MDT-based diffusion distances, and associated embeddings via singular value decompositions. Finally, we propose various strategies for learning MDT operators within the defined operator space, guided by internal quality measures. Beyond enabling flexible model design, MDTs also offer a neutral baseline for evaluating diffusion-based approaches through comparison with randomly selected MDTs. Experiments show the practical impact of the MDT operators in a manifold learning and data clustering context.