mlsanityData to 7 Oct 2026

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

arXiv 2608.21700 ↗First posted 22 Aug 2026quant-ph cs.AI cs.LGcited by 0

On the map: Diffusion models → Diffusion foundations and sampling

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.

Key facts. No citing papers in the map yet (data through 7 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.

Builds on

14 of 50 references.

Closest ancestors · 2

Same direction, newest first

  1. 2025Wavefunction Flows: Efficient Quantum Simulation of Continuous Flow Models9 Oct
  2. 2020Score-Based Generative Modeling through Stochastic Differential Equations26 Nov

Other references · 12

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2022Flow Matching for Generative Modelingcited by 5,426
  3. 2018Neural Ordinary Differential Equationscited by 3,733
  4. 2022Building Normalizing Flows with Stochastic Interpolantscited by 964
  5. 2022Action Matching: Learning Stochastic Dynamics from Samplescited by 94
  6. 2017Unsupervised Generative Modeling Using Matrix Product Statescited by 87
  7. 2019The Born Supremacy: Quantum Advantage and Training of an Ising Born Machinecited by 75
  8. 2018Towards Quantum Machine Learning with Tensor Networkscited by 74
  9. 2018A quantum-inspired classical algorithm for recommendation systemscited by 70
  10. 2019Expressive power of tensor-network factorizations for probabilistic modeling, with applications from hidden Markov models to quantum machine learningcited by 55
  11. 2022Quantum simulation of real-space dynamicscited by 8
  12. 2026Quantum enhanced rare event discovery and samplingcited by 1

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  7. 2023Quantum circuit synthesis with diffusion models
  8. 2026Quantum MeanFlow: single-shot generative sampling on NISQ hardware