# Towards efficient quantum algorithms for diffusion probabilistic models

arXiv: https://arxiv.org/abs/2502.14252 · HTML: https://mlsanity.com/paper/2502.14252/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 29 of its 69 references that are in the map.
- First posted on arXiv 20 Feb 2025.

## Placed in

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

## Builds on (most cited first, 29 of 29)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [DPM-Solver++: Fast Solver for Guided Sampling of Diffusion Probabilistic Models](https://mlsanity.com/paper/2211.01095/) (2022)
- [SNIP: Single-shot Network Pruning based on Connection Sensitivity](https://mlsanity.com/paper/1810.02340/) (2018)
- [Generative Adversarial Networks: An Overview](https://mlsanity.com/paper/1710.07035/) (2017)
- [Fast Sampling of Diffusion Models with Exponential Integrator](https://mlsanity.com/paper/2204.13902/) (2022)
- [Sparsity in Deep Learning: Pruning and growth for efficient inference and training in neural networks](https://mlsanity.com/paper/2102.00554/) (2021)
- [All are Worth Words: A ViT Backbone for Diffusion Models](https://mlsanity.com/paper/2209.12152/) (2022)
- [Pruning neural networks without any data by iteratively conserving synaptic flow](https://mlsanity.com/paper/2006.05467/) (2020)
- [Picking Winning Tickets Before Training by Preserving Gradient Flow](https://mlsanity.com/paper/2002.07376/) (2020)
- [UniPC: A Unified Predictor-Corrector Framework for Fast Sampling of Diffusion Models](https://mlsanity.com/paper/2302.04867/) (2023)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [DPM-Solver-v3: Improved Diffusion ODE Solver with Empirical Model Statistics](https://mlsanity.com/paper/2310.13268/) (2023)
- [Accelerating Diffusion Sampling with Optimized Time Steps](https://mlsanity.com/paper/2402.17376/) (2024)
- [On the Design Fundamentals of Diffusion Models: A Survey](https://mlsanity.com/paper/2306.04542/) (2023)
- [On the Quantum versus Classical Learnability of Discrete Distributions](https://mlsanity.com/paper/2007.14451/) (2020)
- [Towards provably efficient quantum algorithms for large-scale machine-learning models](https://mlsanity.com/paper/2303.03428/) (2023)
- [A comprehensive review of Quantum Machine Learning: from NISQ to Fault Tolerance](https://mlsanity.com/paper/2401.11351/) (2024)
- [The power of block-encoded matrix powers: improved regression techniques via faster Hamiltonian simulation](https://mlsanity.com/paper/1804.01973/) (2018)
- [A Unified Sampling Framework for Solver Searching of Diffusion Probabilistic Models](https://mlsanity.com/paper/2312.07243/) (2023)
- [A super-polynomial quantum-classical separation for density modelling](https://mlsanity.com/paper/2210.14936/) (2022)
- [Quantum Regularized Least Squares](https://mlsanity.com/paper/2206.13143/) (2022)
- [Quantum linear system algorithm with optimal queries to initial state preparation](https://mlsanity.com/paper/2410.18178/) (2024)
- [An unconditional distribution learning advantage with shallow quantum circuits](https://mlsanity.com/paper/2411.15548/) (2024)
- [Fundamental causal bounds of quantum random access memories](https://mlsanity.com/paper/2307.13460/) (2023)

## Built on by (most cited first, 6 of 6)

- [Quantum computing and artificial intelligence: status and perspectives](https://mlsanity.com/paper/2505.23860/) (2025)
- [A PAC-Bayesian approach to generalization for quantum models](https://mlsanity.com/paper/2603.22964/) (2026)
- [Accelerating Inference for Multilayer Neural Networks with Quantum Computers](https://mlsanity.com/paper/2510.07195/) (2025)
- [Optimal algorithmic complexity of inference in quantum kernel methods](https://mlsanity.com/paper/2604.15214/) (2026)
- [Provable learning separation for predicting time-evolution of quantum many-body systems](https://mlsanity.com/paper/2607.06472/) (2026)
- [When AI meets quantum information: A comprehensive review](https://mlsanity.com/paper/2607.00365/) (2026)

## Abstract (arXiv)

A diffusion probabilistic model (DPM) is a generative model renowned for its ability to produce high-quality outputs in tasks such as image and audio generation. However, training DPMs on large, high-dimensional datasets such as high-resolution images or audio incurs significant computational, energy, and hardware costs. In this work, we introduce efficient quantum algorithms for implementing DPMs through various quantum ODE solvers. These algorithms highlight the potential of quantum Carleman linearization for diverse mathematical structures, leveraging state-of-the-art quantum linear system solvers (QLSS) or linear combination of Hamiltonian simulations (LCHS). Specifically, we focus on two approaches: DPM-solver-k which employs exact k-th order derivatives to compute a polynomial approximation of εθ(xλ,λ); and UniPC which uses finite difference of εθ(xλ,λ) at different points (xsm, λsm) to approximate higher-order derivatives. As such, this work represents one of the most direct and pragmatic applications of quantum algorithms to large-scale machine learning models, presumably taking substantial steps towards demonstrating the practical utility of quantum computing.