# Generative quantum machine learning via denoising diffusion probabilistic models

arXiv: https://arxiv.org/abs/2310.05866 · HTML: https://mlsanity.com/paper/2310.05866/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 18 of its 56 references that are in the map.
- First posted on arXiv 9 Oct 2023.

## Placed in

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

## Builds on (most cited first, 18 of 18)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [Noise-Induced Barren Plateaus in Variational Quantum Algorithms](https://mlsanity.com/paper/2007.14384/) (2020)
- [On the relation between optimal transport and Schr"odinger bridges: A stochastic control viewpoint](https://mlsanity.com/paper/1412.4430/) (2014)
- [Layerwise learning for quantum neural networks](https://mlsanity.com/paper/2006.14904/) (2020)
- [Diffusion Probabilistic Models beat GANs on Medical Images](https://mlsanity.com/paper/2212.07501/) (2022)
- [The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine](https://mlsanity.com/paper/1904.02214/) (2019)
- [Out-of-distribution generalization for learning quantum dynamics](https://mlsanity.com/paper/2204.10268/) (2022)
- [Quantum Variational Autoencoder](https://mlsanity.com/paper/1802.05779/) (2018)
- [Do Quantum Circuit Born Machines Generalize?](https://mlsanity.com/paper/2207.13645/) (2022)
- [Learning quantum data with the quantum Earth Mover's distance](https://mlsanity.com/paper/2101.03037/) (2021)
- [Diffusion K-means clustering on manifolds: provable exact recovery via semidefinite relaxations](https://mlsanity.com/paper/1903.04416/) (2019)

## Built on by (most cited first, 30 of 30)

- [Investigating and Mitigating Barren Plateaus in Variational Quantum Circuits: A Survey](https://mlsanity.com/paper/2407.17706/) (2024)
- [Quantum Generative Diffusion Model: A Fully Quantum-Mechanical Model for Generating Quantum State Ensemble](https://mlsanity.com/paper/2401.07039/) (2024)
- [Quantum State Generation with Structure-Preserving Diffusion Model](https://mlsanity.com/paper/2404.06336/) (2024)
- [Local Diffusion Models and Phases of Data Distributions](https://mlsanity.com/paper/2508.06614/) (2025)
- [Quantum-Brain: Quantum-Inspired Neural Network Approach to Vision-Brain Understanding](https://mlsanity.com/paper/2411.13378/) (2024)
- [DiffBatt: A Diffusion Model for Battery Degradation Prediction and Synthesis](https://mlsanity.com/paper/2410.23893/) (2024)
- [Mixed-State Quantum Denoising Diffusion Probabilistic Model](https://mlsanity.com/paper/2411.17608/) (2024)
- [The role of data embedding in equivariant quantum convolutional neural networks](https://mlsanity.com/paper/2312.13250/) (2023)
- [Quantum Flow Matching](https://mlsanity.com/paper/2508.12413/) (2025)
- [Wavefunction Flows: Efficient Quantum Simulation of Continuous Flow Models](https://mlsanity.com/paper/2510.08462/) (2025)
- [Enhancing the Trainability of Variational Quantum Circuits with Regularization Strategies](https://mlsanity.com/paper/2405.01606/) (2024)
- [Overcoming Dimensional Factorization Limits in Discrete Diffusion Models through Quantum Joint Distribution Learning](https://mlsanity.com/paper/2505.05151/) (2025)
- [Physics-inspired Generative AI models via real hardware-based noisy quantum diffusion](https://mlsanity.com/paper/2505.22193/) (2025)
- [Continuous-variable Quantum Diffusion Model for State Generation and Restoration](https://mlsanity.com/paper/2506.19270/) (2025)
- [Quantum Diffusion Model for Quark and Gluon Jet Generation](https://mlsanity.com/paper/2412.21082/) (2024)
- [Superior resilience to poisoning and amenability to unlearning in quantum machine learning](https://mlsanity.com/paper/2508.02422/) (2025)
- [Intrinsic preservation of plasticity in continual quantum learning](https://mlsanity.com/paper/2511.17228/) (2025)
- [Local-Time Riemannian Score Matching on the Quantum Pure-State Manifold](https://mlsanity.com/paper/2605.03573/) (2026)
- [Quantum Generative Diffusion Model for Real-World Time Series](https://mlsanity.com/paper/2606.27561/) (2026)
- [Permutation-equivariant quantum convolutional neural networks](https://mlsanity.com/paper/2404.18198/) (2024)
- [Quantum Implicit Neural Compression](https://mlsanity.com/paper/2412.19828/) (2024)
- [Learning Relationship between Quantum Walks and Underdamped Langevin Dynamics](https://mlsanity.com/paper/2601.01589/) (2026)
- [Universality of Many-body Projected Ensemble for Learning Quantum Data Distribution](https://mlsanity.com/paper/2601.18637/) (2026)
- [Learning Quantum Data Distribution via Chaotic Quantum Diffusion Model](https://mlsanity.com/paper/2602.22061/) (2026)
- [Toward Generative Quantum Utility via Correlation-Complexity Map](https://mlsanity.com/paper/2603.06440/) (2026)
- [Intrinsic Flow Matching on Quantum Pure-State Manifolds with Phase-Aligned Transport](https://mlsanity.com/paper/2606.21256/) (2026)
- [An Hybrid Quantum-Classical Diffusion Model for Image Generation](https://mlsanity.com/paper/2607.07072/) (2026)
- [Quantum MeanFlow: single-shot generative sampling on NISQ hardware](https://mlsanity.com/paper/2609.02186/) (2026)
- [Conditional Quantum Flow Matching for Data-Scarce Physiological Signal Augmentation](https://mlsanity.com/paper/2609.14019/) (2026)
- [Quantum Diffusion Models for Medical Image Analysis](https://mlsanity.com/paper/2609.31070/) (2026)

## Abstract (arXiv)

Deep generative models are key-enabling technology to computer vision, text generation, and large language models. Denoising diffusion probabilistic models (DDPMs) have recently gained much attention due to their ability to generate diverse and high-quality samples in many computer vision tasks, as well as to incorporate flexible model architectures and a relatively simple training scheme. Quantum generative models, empowered by entanglement and superposition, have brought new insight to learning classical and quantum data. Inspired by the classical counterpart, we propose the quantum denoising diffusion probabilistic model (QuDDPM) to enable efficiently trainable generative learning of quantum data. QuDDPM adopts sufficient layers of circuits to guarantee expressivity, while it introduces multiple intermediate training tasks as interpolation between the target distribution and noise to avoid barren plateau and guarantee efficient training. We provide bounds on the learning error and demonstrate QuDDPM's capability in learning correlated quantum noise model, quantum many-body phases, and topological structure of quantum data. The results provide a paradigm for versatile and efficient quantum generative learning.