# Scalable quantum simulation of continuous-time generative models via tensor networks

arXiv: https://arxiv.org/abs/2608.21700 · HTML: https://mlsanity.com/paper/2608.21700/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 14 of its 50 references that are in the map.
- First posted on arXiv 22 Aug 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Action Matching: Learning Stochastic Dynamics from Samples](https://mlsanity.com/paper/2210.06662/) (2022)
- [Unsupervised Generative Modeling Using Matrix Product States](https://mlsanity.com/paper/1709.01662/) (2017)
- [Towards Quantum Machine Learning with Tensor Networks](https://mlsanity.com/paper/1803.11537/) (2018)
- [The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine](https://mlsanity.com/paper/1904.02214/) (2019)
- [A quantum-inspired classical algorithm for recommendation systems](https://mlsanity.com/paper/1807.04271/) (2018)
- [Expressive power of tensor-network factorizations for probabilistic modeling, with applications from hidden Markov models to quantum machine learning](https://mlsanity.com/paper/1907.03741/) (2019)
- [Quantum simulation of real-space dynamics](https://mlsanity.com/paper/2203.17006/) (2022)
- [Wavefunction Flows: Efficient Quantum Simulation of Continuous Flow Models](https://mlsanity.com/paper/2510.08462/) (2025)
- [Quantum enhanced rare event discovery and sampling](https://mlsanity.com/paper/2606.06316/) (2026)

## Abstract (arXiv)

Continuous-time flow and diffusion models are widely used across many application domains, from large-scale deployment in computer vision and protein folding to emerging adoption for modeling language, time series, and quantum states. After training, inferring statistical properties from continuous-time models is costly. Wavefunction flows target this cost by recasting learned transport as unitary evolution, whose final Born distribution approximates the target distribution. This prepares a coherent amplitude encoding (a qsample) that can be post-processed by quantum algorithms offering a quadratic advantage over Monte Carlo sampling. We present the first numerical study of these flows, in which we represent time-dependent potentials and states as tensor networks. At spatial dimension d=8, storage falls by ~ 107× relative to the dense grid of Nd points, and evolution wall-clock time falls by gtrsim 103× against a baseline extrapolated from the measured d≤ 5 scaling. We validate our pipeline by reproducing the O(1/√prm rare) scaling of rare-event sampling.