# Mixed-State Quantum Denoising Diffusion Probabilistic Model

arXiv: https://arxiv.org/abs/2411.17608 · HTML: https://mlsanity.com/paper/2411.17608/

## 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 24 of its 54 references that are in the map.
- First posted on arXiv 26 Nov 2024.

## Placed in

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

## Builds on (most cited first, 24 of 24)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Jukebox: A Generative Model for Music](https://mlsanity.com/paper/2005.00341/) (2020)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [The Marginal Value of Adaptive Gradient Methods in Machine Learning](https://mlsanity.com/paper/1705.08292/) (2017)
- [On the Importance of Noise Scheduling for Diffusion Models](https://mlsanity.com/paper/2301.10972/) (2023)
- [A Survey on Neural Speech Synthesis](https://mlsanity.com/paper/2106.15561/) (2021)
- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [gDDIM: Generalized denoising diffusion implicit models](https://mlsanity.com/paper/2206.05564/) (2022)
- [AUC Maximization in the Era of Big Data and AI: A Survey](https://mlsanity.com/paper/2203.15046/) (2022)
- [Experimental Quantum Generative Adversarial Networks for Image Generation](https://mlsanity.com/paper/2010.06201/) (2020)
- [Quantum Variational Autoencoder](https://mlsanity.com/paper/1802.05779/) (2018)
- [Generative quantum machine learning via denoising diffusion probabilistic models](https://mlsanity.com/paper/2310.05866/) (2023)
- [Quantum-Noise-Driven Generative Diffusion Models](https://mlsanity.com/paper/2308.12013/) (2023)
- [Quantum State Generation with Structure-Preserving Diffusion Model](https://mlsanity.com/paper/2404.06336/) (2024)

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

- [Overcoming Dimensional Factorization Limits in Discrete Diffusion Models through Quantum Joint Distribution Learning](https://mlsanity.com/paper/2505.05151/) (2025)
- [Local-Time Riemannian Score Matching on the Quantum Pure-State Manifold](https://mlsanity.com/paper/2605.03573/) (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)
- [Quantum Diffusion Models for Medical Image Analysis](https://mlsanity.com/paper/2609.31070/) (2026)

## Abstract (arXiv)

Generative quantum machine learning has gained significant attention for its ability to produce quantum states with desired distributions. Among various quantum generative models, quantum denoising diffusion probabilistic models (QuDDPMs) [Phys. Rev. Lett. 132, 100602 (2024)] provide a promising approach with stepwise learning that resolves the training issues. However, the requirement of high-fidelity scrambling unitaries in QuDDPM poses a challenge in near-term implementation. We propose the textitmixed-state quantum denoising diffusion probabilistic model (MSQuDDPM) to eliminate the need for scrambling unitaries. Our approach focuses on adapting the quantum noise channels to the model architecture, which integrates depolarizing noise channels in the forward diffusion process and parameterized quantum circuits with projective measurements in the backward denoising steps. We also introduce several techniques to improve MSQuDDPM, including a cosine-exponent schedule of noise interpolation, the use of single-qubit random ancilla, and superfidelity-based cost functions to enhance the convergence. We evaluate MSQuDDPM on quantum ensemble generation tasks, demonstrating its successful performance.