# Stochastics of shapes and Kunita flows

arXiv: https://arxiv.org/abs/2512.11676 · HTML: https://mlsanity.com/paper/2512.11676/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 49 references that are in the map.
- First posted on arXiv 12 Dec 2025.

## Builds on (most cited first, 10 of 10)

- [Elastic shape analysis of surfaces with second-order Sobolev metrics: a comprehensive numerical framework](https://mlsanity.com/paper/2204.04238/) (2022)
- [Conditioning non-linear and infinite-dimensional diffusion processes](https://mlsanity.com/paper/2402.01434/) (2024)
- [Diffusion bridges for stochastic Hamiltonian systems and shape evolutions](https://mlsanity.com/paper/2002.00885/) (2020)
- [Intrinsic Riemannian Functional Data Analysis](https://mlsanity.com/paper/1812.01831/) (2018)
- [A Geometric Framework for Stochastic Shape Analysis](https://mlsanity.com/paper/1703.09971/) (2017)
- [Bridge Simulation and Metric Estimation on Landmark Manifolds](https://mlsanity.com/paper/1705.10943/) (2017)
- [Higher-order Spatial Accuracy in Diffeomorphic Image Registration](https://mlsanity.com/paper/1412.7504/) (2014)
- [Spherical Autoregressive Models, With Application to Distributional and Compositional Time Series](https://mlsanity.com/paper/2203.12783/) (2022)
- [Backward Filtering Forward Guiding](https://mlsanity.com/paper/2505.18239/) (2025)
- [A function space perspective on stochastic shape evolution](https://mlsanity.com/paper/2302.05382/) (2023)

## Built on by (most cited first, 2 of 2)

- [Neural Backward Filtering Forward Guiding](https://mlsanity.com/paper/2601.23030/) (2026)
- [Landmark shape spaces with induced metrics](https://mlsanity.com/paper/2607.28064/) (2026)

## Abstract (arXiv)

Stochastic processes of evolving shapes are used in applications including evolutionary biology, where morphology changes stochastically as a function of evolutionary processes. Due to the non-linear and often infinite-dimensional nature of shape spaces, the mathematical construction of suitable stochastic shape processes is far from immediate. We define and formalize properties that stochastic shape processes should ideally satisfy to be compatible with the shape structure, and we link this to Kunita flows that, when acting on shape spaces, induce stochastic processes that satisfy these criteria by their construction. We couple this with a survey of other relevant shape stochastic processes and show how bridge sampling techniques can be used to condition shape stochastic processes on observed data thereby allowing for statistical inference of parameters of the stochastic dynamics.