# Continuous-variable Quantum Diffusion Model for State Generation and Restoration

arXiv: https://arxiv.org/abs/2506.19270 · HTML: https://mlsanity.com/paper/2506.19270/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 13 of its 40 references that are in the map.
- First posted on arXiv 24 Jun 2025.

## Placed in

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

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [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)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Diffusion Models in Vision: A Survey](https://mlsanity.com/paper/2209.04747/) (2022)
- [MotionDiffuse: Text-Driven Human Motion Generation with Diffusion Model](https://mlsanity.com/paper/2208.15001/) (2022)
- [Restoring Vision in Adverse Weather Conditions with Patch-Based Denoising Diffusion Models](https://mlsanity.com/paper/2207.14626/) (2022)
- [Diffusion Models for Imperceptible and Transferable Adversarial Attack](https://mlsanity.com/paper/2305.08192/) (2023)
- [Continuous-variable quantum neural networks](https://mlsanity.com/paper/1806.06871/) (2018)
- [Generative quantum machine learning via denoising diffusion probabilistic models](https://mlsanity.com/paper/2310.05866/) (2023)
- [Stimulating Diffusion Model for Image Denoising via Adaptive Embedding and Ensembling](https://mlsanity.com/paper/2307.03992/) (2023)
- [Quantum Generative Diffusion Model: A Fully Quantum-Mechanical Model for Generating Quantum State Ensemble](https://mlsanity.com/paper/2401.07039/) (2024)

## Built on by (most cited first, 2 of 2)

- [When AI meets quantum information: A comprehensive review](https://mlsanity.com/paper/2607.00365/) (2026)
- [Quantum Diffusion Models for Medical Image Analysis](https://mlsanity.com/paper/2609.31070/) (2026)

## Abstract (arXiv)

The generation and preservation of complex quantum states against environmental noise are paramount challenges in advancing continuous-variable (CV) quantum information processing. This paper introduces a novel framework based on continuous-variable quantum diffusion principles, synergizing them with CV quantum neural networks (CVQNNs) to address these dual challenges. For the task of state generation, our Continuous-Variable Quantum Diffusion Generative model (CVQD-G) employs a physically driven forward diffusion process using a thermal loss channel, which is then inverted by a learnable, parameter-efficient backward denoising process based on a CVQNN with time-embedding. This framework's capability is further extended for state recovery by the Continuous-Variable Quantum Diffusion Restoration model (CVQD-R), a specialized variant designed to restore quantum states, particularly coherent states with unknown parameters, from thermal degradation. Extensive numerical simulations validate these dual capabilities, demonstrating the high-fidelity generation of diverse Gaussian (coherent, squeezed) and non-Gaussian (Fock, cat) states, typically with fidelities exceeding 99%, and confirming the model's ability to robustly restore corrupted states. Furthermore, a comprehensive complexity analysis reveals favorable training and inference costs, highlighting the framework's efficiency, scalability, and its potential as a robust tool for quantum state engineering and noise mitigation in realistic CV quantum systems.