# Quantum Generative Diffusion Model: A Fully Quantum-Mechanical Model for Generating Quantum State Ensemble

arXiv: https://arxiv.org/abs/2401.07039 · HTML: https://mlsanity.com/paper/2401.07039/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 42 of its 103 references that are in the map.
- First posted on arXiv 13 Jan 2024.

## Placed in

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

## Builds on (most cited first, 30 of 42)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Understanding Diffusion Models: A Unified Perspective](https://mlsanity.com/paper/2208.11970/) (2022)
- [Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models](https://mlsanity.com/paper/2103.04922/) (2021)
- [A Comprehensive Survey of AI-Generated Content (AIGC): A History of Generative AI from GAN to ChatGPT](https://mlsanity.com/paper/2303.04226/) (2023)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Quantum generative adversarial networks](https://mlsanity.com/paper/1804.08641/) (2018)
- [Discrete Variational Autoencoders](https://mlsanity.com/paper/1609.02200/) (2016)
- [Differentiable Learning of Quantum Circuit Born Machine](https://mlsanity.com/paper/1804.04168/) (2018)
- [Robust data encodings for quantum classifiers](https://mlsanity.com/paper/2003.01695/) (2020)
- [Experimental Quantum Generative Adversarial Networks for Image Generation](https://mlsanity.com/paper/2010.06201/) (2020)
- [Quantum circuit architecture search for variational quantum algorithms](https://mlsanity.com/paper/2010.10217/) (2020)
- [Reinforcement learning for optimization of variational quantum circuit architectures](https://mlsanity.com/paper/2103.16089/) (2021)
- [The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine](https://mlsanity.com/paper/1904.02214/) (2019)
- [Quantum Variational Autoencoder](https://mlsanity.com/paper/1802.05779/) (2018)
- [Recent Advances for Quantum Neural Networks in Generative Learning](https://mlsanity.com/paper/2206.03066/) (2022)
- [Quantum Wasserstein Generative Adversarial Networks](https://mlsanity.com/paper/1911.00111/) (2019)
- [Generative quantum machine learning via denoising diffusion probabilistic models](https://mlsanity.com/paper/2310.05866/) (2023)
- [Learning and Inference on Generative Adversarial Quantum Circuits](https://mlsanity.com/paper/1808.03425/) (2018)
- [Hybrid Quantum-Classical Generative Adversarial Network for High Resolution Image Generation](https://mlsanity.com/paper/2212.11614/) (2022)

## Built on by (most cited first, 9 of 9)

- [Quantum Generative Adversarial Autoencoders: Learning latent representations for quantum data generation](https://mlsanity.com/paper/2509.16186/) (2025)
- [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)
- [Model selection in hybrid quantum neural networks with applications to quantum transformer architectures](https://mlsanity.com/paper/2603.21749/) (2026)
- [Local-Time Riemannian Score Matching on the Quantum Pure-State Manifold](https://mlsanity.com/paper/2605.03573/) (2026)
- [Mitigating Barren Plateaus in Quantum Denoising Diffusion Probabilistic Model](https://mlsanity.com/paper/2512.06695/) (2025)
- [Intrinsic Flow Matching on Quantum Pure-State Manifolds with Phase-Aligned Transport](https://mlsanity.com/paper/2606.21256/) (2026)
- [Quantum Diffusion Models for Medical Image Analysis](https://mlsanity.com/paper/2609.31070/) (2026)

## Abstract (arXiv)

Mixed quantum states are the native description of many physically important quantum systems, making their generation a fundamental task in quantum information processing. However, constructing a diffusion process that generates density operators while keeping every reverse step physically valid remains nontrivial. This work introduces Quantum Generative Diffusion Model (QGDM), a fully quantum-mechanical model whose forward and backward processes are grounded in quantum channel theory. Through a non-unitary forward process, any target quantum state can be transformed into a completely mixed state. A trainable backward process recovers the former from the latter. We introduce partial trace to make the backward process non-unitary, and share parameters across timesteps by incorporating temporal information as an input. We present QGDM's resource-efficient version to reduce auxiliary qubits while preserving generative capabilities. We theoretically analyze the denoising design, showing it avoids a low-loss shortcut that traps training and cause generation failure. Simulations confirm that QGDM outperforms quantum generative adversarial networks on random pure- and mixed-state generation, with better noise robustness than other quantum generative models and a task-specialized approach for practical Gibbs state generation. Hence, QGDM provides a channel-based diffusion framework for learning fixed mixed-state targets, extending quantum generative modeling toward realistic quantum information settings.