⚡ electrical engineering

Quantum Diffusion Models for Medical Image Analysis

This paper introduces a scalable hybrid Quantum Diffusion Model that utilizes a Discrete-Time Quantum Walk on a real quantum device for forward dynamics and a classical learning model for backward denoising, successfully demonstrating competitive performance in generating large-scale medical images (including 2D and 3D volumes) compared to classical counterparts.

Original authors: Francesco Aldo Venturelli, Stefano Martina, Marco Parigi, Filippo Caruso, Alba Cervera-Lierta, Miguel A. González Ballester

Published 2026-09-28

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CC BY 4.0

Original authors: Francesco Aldo Venturelli, Stefano Martina, Marco Parigi, Filippo Caruso, Alba Cervera-Lierta, Miguel A. González Ballester

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the rapidly evolving world of artificial intelligence, a powerful new tool has emerged for creating images: the diffusion model. Imagine a process where a clear picture is slowly turned into static, like a television losing its signal, until only random noise remains. Scientists have learned how to reverse this process, teaching a computer to start with that static and gradually peel away the noise to reveal a coherent image. This technique has become a cornerstone of modern image generation, helping to create everything from artistic renderings to synthetic medical data for research. However, running these complex simulations requires immense computing power, often straining the limits of traditional machines. At the same time, a different field of computing is rising, one that uses the strange rules of quantum mechanics to solve problems that are impossible for standard computers. Quantum computers use tiny units of information called qubits, which can exist in multiple states at once, offering a potential shortcut for heavy calculations. The challenge has been that current quantum machines are still in their early, noisy stages, making them difficult to use for large-scale tasks like processing high-resolution medical scans.

A team of researchers has now bridged these two worlds by creating a hybrid system that uses a real quantum computer to handle the messy part of the image generation process, while a traditional computer handles the cleanup. Their work demonstrates that it is possible to use today's imperfect quantum devices to model the forward diffusion process—the step where an image is corrupted by noise—without needing the error-correction technology that is not yet available. Instead of fighting the natural noise of the quantum machine, the researchers turned it into a feature, using the machine's inherent instability to help scatter the image data into randomness. They then trained a classical neural network, a type of artificial intelligence, to learn how to reverse this specific quantum noise and reconstruct the original image. The team tested this approach on three different types of medical data: small color images of blood cells, large grayscale scans of human brains, and three-dimensional volumes of rib fractures.

The results show that this hybrid method is competitive with purely classical approaches, even when dealing with complex, three-dimensional medical volumes. For the brain scans and the rib fracture data, the quantum-assisted model produced images that were structurally very similar to the real scans, matching the quality of the best traditional models. In fact, for the three-dimensional rib fracture volumes, the hybrid model generated data that was statistically closer to the original distribution than the classical version. The researchers found that the quantum process was particularly good at preserving the structural details of the images, such as the shapes of brain ventricles or the texture of bone fractures. This suggests that the unique way quantum noise spreads information might actually help create more realistic medical images than standard methods in certain scenarios.

The study relied on a specific quantum algorithm called a discrete-time quantum walk, which acts like a random walker moving along a chain of possibilities. In this setup, each pixel of a medical image is assigned to a quantum walker that moves back and forth, its position representing the brightness or color of that pixel. The researchers ran this process on a real quantum computer with 133 qubits, selecting a small group of connected qubits to act as the walker and a "coin" that decides its direction. Because the machine is noisy, the walker does not move perfectly; it jitters and drifts, which is exactly what the diffusion model needs to turn a clear image into noise. The team processed images with up to 64 different intensity levels and volumes made of thousands of tiny 3D pixels. They found that by carefully managing the quantum hardware and using a classical computer to learn the reversal, they could generate new, synthetic medical images that looked and behaved like real patient data.

While the system showed great promise, the researchers noted that the performance varied depending on the type of image. For the smaller, lower-resolution blood cell images, the structural similarity was slightly lower than what some other studies have achieved with different setups. However, the authors explained that this was likely due to the lower resolution and fewer color levels in their specific dataset, rather than a failure of the quantum method itself. The study serves as a proof of concept, showing that current, imperfect quantum computers can be useful tools for medical imaging tasks. It suggests that we do not need to wait for perfect, error-free quantum machines to begin exploring their potential in healthcare. By combining the raw, noisy power of today's quantum hardware with the precision of classical learning, scientists can now process real-world medical data in ways that were previously thought to be out of reach.

Technical Summary: Quantum Diffusion Models for Medical Image Analysis

Problem Statement
Generative AI, particularly Diffusion Models (DMs), has achieved state-of-the-art performance in medical image analysis, including synthetic data generation and reconstruction. However, existing Quantum Machine Learning (QML) approaches for image analysis are severely limited by the constraints of current Noisy Intermediate-Scale Quantum (NISQ) devices. Most prior attempts restrict data dimensionality significantly or rely on hybrid frameworks where only the backward (denoising) process is quantum-enhanced, leaving the forward diffusion process classical. Furthermore, previous works applying Quantum Diffusion Models (QDMs) to medical imaging have utilized classical U-Net architectures enhanced with quantum layers solely for the backward process, failing to leverage the intrinsic properties of quantum hardware for the forward dynamics.

Methodology
The authors propose a scalable Hybrid Quantum Diffusion Model that uniquely assigns the forward diffusion process to a real quantum device and the backward denoising process to a classical learning model.

Quantum Forward Process:
- The method employs a Discrete-Time Quantum Walk (DTQW) executed on a real NISQ device (specifically the IBM ibm_torino processor).
- Input image pixels (or voxels) are discretized into intensity levels ( $0, \dots, 2^{N_q}-1$ ) and mapped to quantum states.
- The system utilizes a "ring-chain" Markov process topology, where a quantum walker moves along a chain of intensity levels. A "coin" qubit (in superposition) dictates the direction of the walk.
- Crucially, the authors exploit the intrinsic quantum noise of the NISQ device as a necessary resource. While pure unitary dynamics would prevent convergence to a uniform distribution, the natural decoherence and noise of the hardware facilitate the transition to the required uniform prior distribution ( $p(x_T)$ ).
- The forward dynamics are simulated via a quantum channel $\mathcal{E}$ applied to the unitary evolution $U_t$ , formalized as $\rho_t = \mathcal{E}(U_t \rho_0 U_t^\dagger)$ .
- To handle large images, the process is parallelized: each pixel/channel undergoes an independent DTQW. The authors increased the intensity levels from 8 to 64 compared to previous work, utilizing Qiskit optimization levels to mitigate gate counts.
Classical Backward Process:
- A U-Net architecture is trained to reverse the diffusion process, predicting the clean data $x_{t-1}$ from the noisy state $x_t$ .
- The authors propose two specific architectures:
  - A 2D U-Net for grayscale and RGB images, featuring time embedding in encoder layers and a shallow bottleneck.
  - A 3D U-Net for volumetric data, featuring time embedding in both encoder and decoder layers, a deeper bottleneck, and SiLU activation functions for gradient stability.
- Training involves minimizing a loss function between the reference noisy pixel values and the U-Net's reconstruction. For the BraTS2020 dataset, a hybrid loss combining Cross-Entropy and Kullback-Leibler (KL) divergence is used to better match pixel-value distributions.
Datasets and Evaluation:
- The model was tested on three distinct medical datasets: BloodMNIST (3,329 RGB images, $64\times64$ ), BraTS2020 (484 grayscale MRI slices, $190\times190$ ), and FractureMNIST3D (1,370 3D CT volumes, $28\times28\times28$ ).
- Performance was evaluated using three metrics: KL Divergence (distributional alignment), Fréchet Inception Distance (FID) (generative quality), and Structural Similarity Index Measure (SSIM) (structural fidelity).
- Experiments were conducted both via classical simulation of the QDM and experimental implementation on the real quantum device with error mitigation techniques.

Key Contributions

Novel Architecture: Unlike previous QDMs that use quantum layers only for the backward pass, this work implements a quantum forward process on real hardware, leveraging the device's intrinsic noise to drive the diffusion toward a uniform distribution.
Scalability to Real-World Data: The method successfully processes moderate-sized, real-world medical data, including RGB images and 3D volumes, overcoming the dimensionality limitations typical of NISQ-based QML.
Methodological Improvements: The study introduces significant enhancements over the authors' prior work [50], including increased intensity levels (up to 64), exploration of different quantum noise topologies, and advanced U-Net architectures with tailored time embeddings.
Benchmarking: The paper provides a rigorous comparison against a classical counterpart (discrete-state space DMs), demonstrating that the hybrid approach yields competitive results.

Results

Performance Metrics: The hybrid quantum model demonstrated competitive performance against the classical baseline.
- On FractureMNIST3D, the quantum model achieved lower KL divergence and FID scores than the classical model, with equal SSIM.
- Across all three datasets, the quantum model consistently achieved higher SSIM values than the classical counterpart, suggesting that the quantum forward process may help preserve structural features in the generated data.
- For BloodMNIST and BraTS2020, the quantum model showed higher FID scores. The authors attribute this to the FID metric's reliance on a network pre-trained on generic high-quality data, which may not be optimal for specialized medical datasets with specific quantization and resolution constraints.
Visual Analysis: Qualitative results (PCA and KDE plots) indicate that the model successfully learns the data distribution modes. For BloodMNIST, it captures multiple modes; for BraTS2020, it avoids model collapse despite a single-mode distribution. Visual samples show the generation of anatomically plausible structures, including blood cells, brain ventricles, and tumor masses.

Significance and Claims
The authors position this work as a proof of concept for the applicability of current NISQ devices in healthcare. They claim that their approach circumvents the need for error-correcting codes by turning the "detrimental" quantum noise into a functional component of the generative process.

The paper modestly asserts that while the model is in an early stage and results are comparable to (rather than vastly superior to) existing classical or hybrid methods, the ability to process complex, multi-dimensional medical data (RGB and 3D volumes) on real quantum hardware is a significant step forward. The work aims to contribute to the research and development of medical applications using quantum computers, specifically testing the capabilities of current NISQ devices on critical, resource-intensive problems without requiring full fault tolerance.

Technical Summary: Quantum Diffusion Models for Medical Image Analysis

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