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Hybrid Quantum-Classical Latent Diffusion Models for Medical Image Generation
Kübra Yeter-Aydeniz, Nora M. Bauer, Pranay Jain, Max Masnick
TL;DR
Medical image generation needs diverse, realistic training images, while prior quantum generative studies had not reached industry-relevant scale. This paper tests a quantum-enhanced diffusion model with a quantum VAE on retinal fundus images, reporting the highest gradable-image percentage for QD+QVAE and the closest overall match to the real-image distribution. The authors identify quantum diffusion as a target for further research on industrially relevant generative modeling.
Problem
Medical image generation needs diverse, realistic images, and prior quantum diffusion studies had not reached large-scale, industry-relevant applications.
Source: §I · pp. 1–2Method
The paper combines quantum components in a DDPM and VAE to generate retinal fundus images.
Source: §I · p. 2Results
QD+QVAE produces the highest percentage of gradable images and matches the real image distribution most closely with the lowest MSE.
Source: A. Noiseless Simulation Results · pp. 5–6Takeaways & Limitations
The authors identify quantum diffusion models as strong candidates for further research on near-term quantum utility in industrial image generation.
Source: §I · p. 2Automorph was designed to assess retinal feature measurement on real images, rather than to validate synthetic images strictly.
Source: §III · p. 4
Abstract
from arXiv · showhide
Generative learning models in medical research are crucial in developing training data for deep learning models and advancing diagnostic tools, but the problem of high-quality, diverse images is an open topic of research. Quantum-enhanced generative models have been proposed and tested in the literature but have been restricted to small problems below the scale of industry relevance. In this paper, we propose quantum-enhanced diffusion and variational autoencoder (VAE) models and test them on the fundus retinal image generation task. In our numerical experiments, the images generated using quantum-enhanced models are of higher quality, with 86% classified as gradable by external validation compared to 69% with the classical model, and they match more closely in features to the real image distribution compared to the ones generated using classical diffusion models, even when the classical diffusion models are larger than the quantum model. Additionally, we perform noisy testing to confirm the numerical experiments, finding that quantum-enhanced diffusion model can sometimes produce higher quality images, both in terms of diversity and fidelity, when tested with quantum hardware noise. Our results indicate that quantum diffusion models on current quantum hardware are strong targets for further research on quantum utility in generative modeling for industrially relevant problems.
I. INTRODUCTION
The paper targets diverse, realistic retinal fundus image generation and extends quantum diffusion research toward industry-relevant medical imaging. It reports higher image quality than classical DDPMs, including when the classical models use more layers.
I. INTRODUCTION
- Retinal fundus generation needs diverse, realistic images for diagnosis and research, while prior GAN-generated fundus images lacked diversity.Medical training data is also limited by cost, patient privacy, and availability.Source: §I · p. 1
- DDPMs have been used for diverse medical image generation and fundus-specific synthesis, while quantum generative work includes hybrid GANs and quantum diffusion models.A quantum GAN for knee X-rays outperformed classical WGAN, but PCA limited image quality and colored-image generalization was challenging.Source: §I · pp. 1–2
- Prior quantum diffusion studies explored several applications but had not reached large-scale, industry-relevant applications.Those studies included quantum data, differential equations, circuit synthesis, and MNIST- and EuroCon-type images.Source: §I · p. 2
- The proposed model combines quantum components in both the DDPM and VAE for an industrially relevant medical image-generation task.Figure 1 depicts the QVAE and QDDPM structures alongside ResBlock, QResBlock, and QUBlock.Source: §I · p. 2, Figure 1 · p. 2
- Quantum-enhanced DDPMs produce higher-quality images than classical DDPMs, even when the classical models add layers.Noisy simulations and hardware testing also indicate noise resilience and maintained image quality when simulated noise is added.Source: §I · p. 2
II. METHODS
The method combines a VAE’s latent-space compression with a DDPM that learns to remove noise iteratively. Quantum components are added to both parts to increase expressivity and capture richer correlations.
II. METHODS
- A classical latent diffusion model pairs a VAE-compressed latent space with a DDPM trained to reverse an iterative noise process.The forward process adds noise to an image; the reverse process learns to remove it to generate images from noise.Source: §II · pp. 2–3
- The proposed QVAE and QDDPM add quantum components to the classical model to capture richer correlations and provide extra expressivity.The authors state that this makes the latent distribution more amenable to diffusion.Source: §II · p. 3
A. Quantum Variational Autoencoder (QVAE)
The QVAE compresses fundus images into a smaller latent representation and reconstructs them through an encoder-decoder structure. Its quantum blocks augment standard residual and UNet blocks.
A. Quantum Variational Autoencoder (QVAE)
- The QVAE compresses 1024×1024 fundus images into a 128×128 latent space.Its encoder uses a QUBlock, Down and ResBlock layers, and a Basic Block; the decoder upsamples through convolutional, ResBlock, and Up layers.Source: A. Quantum Variational Autoencoder… · p. 3
- A QResBlock is a standard ResBlock enhanced with two quantum layers, and a QUBlock replaces standard ResBlocks with QResBlocks.Removing the quantum layers from a QResBlock recovers the standard ResBlock.Source: A. Quantum Variational Autoencoder… · p. 3
- During QVAE training, data passes directly from the encoder to the decoder, which is trained using Adam at a learning rate of 0.001.Source: A. Quantum Variational Autoencoder… · p. 3
B. Quantum DDPM
The QDDPM corrupts images with Gaussian noise in latent space and trains a UNet-based noise estimator to reverse that process. Its generated latent image is decoded back into two-dimensional image space.
B. Quantum DDPM
- The QDDPM applies a 1000-step Gaussian diffusion process in latent space, then uses a UNet to estimate and iteratively remove the added noise.The UNet includes five QUBlocks, two QResBlocks, and label embedding in its QUBlocks.Source: B. Quantum DDPM · p. 3
- After denoising, the generated latent image passes through the decoder to return a 2D image, and the QUNet is trained with AdamW at a learning rate of 0.001.Source: B. Quantum DDPM · p. 3
C. Quantum Layer Design
The section compares five quantum-layer ansätze for expressive power, trainability, and hardware efficiency, then selects ESE2 based on its combined performance under simulated hardware noise and gradient-variance scaling.
C. Quantum Layer Design
- The study compares five ansätze—S2D, BE, SE, ESE, and ESE2—using hardware-noise robustness, entanglement entropy, and gradient variance.The target is IBM Quantum Cleveland; gradient variance is used to assess trainability and its tendency toward barren plateaus.Source: C. Quantum Layer Design · p. 3
- ESE2 encodes the most parameters at the lowest noisy Hamming distance, while its gradient variance shrinks more slowly than SE and ESE1.Its gradient-variance slope is −0.79, compared with −1.19 for SE and −1.09 for ESE1, indicating potential trainability at larger sizes.Source: C. Quantum Layer Design · p. 4
- Measurement-error mitigation with M3 slightly lowers noisy Hamming distance across the layer designs.The protocol uses a confusion matrix to correct measured false-positive and false-negative rates.Source: C. Quantum Layer Design · p. 4
III. NUMERICAL RESULTS
The numerical study uses selected RFMID retinal-image classes and several distributional and image-quality metrics, including Automorph grading as a proxy for synthetic-image quality. The supplied passages describe the evaluation setup and a circuit-design figure, but do not report the numerical model-comparison outcomes.
III. NUMERICAL RESULTS
- The evaluation uses RFMID classes 0, 1, and 2, the dataset’s largest classes, from a 3,200-image dataset split into training, validation, and testing sets.The splits contain 1,920, 640, and 640 images, respectively.Source: §III · p. 4
- Model evaluation includes FID, CMMD, recall, precision, Inception Score, and Automorph grading.FID estimates the gap between generated and real image distributions; CMMD measures feature-space distribution similarity, while precision and recall assess support coverage.Source: §III · p. 4
- Automorph grades images as gradable or ungradable before computing 72 anatomical-feature metrics on gradable images, but it is only a proxy for synthetic-image quality.It was designed to assess gradability for retinal-feature measurement on real images, not specifically to validate synthetic images.Source: §III · p. 4
- Figure 2 summarizes ansatz structure, gradient-variance slopes, noisy Hamming distance, and noiseless entanglement entropy across circuit designs.Its panels show a four-qubit, two-layer ESE2 circuit; gradient variance versus qubit count; and Hamming distance and entropy versus encoded parameter count.Source: Figure 2 · p. 5
A. Noiseless Simulation Results
In noiseless simulations, QD+QVAE led on Automorph gradability and most closely matched real images across measured eye-feature distributions. Results varied by metric, and Automorph was not designed specifically to validate generative image quality.
A. Noiseless Simulation Results
- For the 12-qubit, 6-layer model, CDCNN was added for a fair model-size comparison, but added 16,384 parameters versus 216 quantum parameters—a 75× overshoot.Source: A. Noiseless Simulation Results · p. 5
- QD+QVAE produced the highest percentage of gradable images among the tested models, according to Automorph grading.The authors caution that Automorph measures retinal features and is not strictly a generative-model validation tool.Source: A. Noiseless Simulation Results · p. 5, Table I · p. 6
- Over 80% of QD+QVAE images had > 0.5 “softmax good” confidence, the highest share among the tested models.The figure compares sorted confidence values for 208 Class 0 images from five models and the real-image set.Source: A. Noiseless Simulation Results · pp. 5–6, Figure 3 · p. 6
- QD+QVAE achieved the lowest overall feature-distribution MSE and performed best on whole-image vascular metrics and Zones B and C.CD+QVAE performed best in the Disc/Cup category, while QD+CVAE performed best in Zone B.Source: A. Noiseless Simulation Results · p. 6, Table II · p. 6
B. Noisy Simulation Results
In noisy simulations, readout-error models sometimes outperformed the noiseless model across the evaluated metrics. The best-performing error setting differed by metric in the 8-qubit tests.
B. Noisy Simulation Results
- The authors tested readout and statistical noise because quantum noise is inherent to current devices and may also benefit diffusion sampling.Prior work proposed quantum-noise-based generative diffusion for sampling more complex probability distributions.Source: B. Noisy Simulation Results · p. 7
- For the 8-qubit model, the noiseless model did not outperform readout-error models on any metric.The best readout-error setting varied: 10% led on Automorph grading and IS, 5% on precision and recall, and 2.5% on FID and CMMD.Source: B. Noisy Simulation Results · p. 7
- The noisy tests used 1000-shot expectation values, with readout-error probabilities of 2.5%, 5%, and 10%.Earlier numerical experiments used statevector simulations with exact expectation values.Source: B. Noisy Simulation Results · p. 7
C. Small Datasets
On a randomly selected quarter-size RFMID training set, quantum-enhanced models retained strong performance. The QVAE showed larger advantages over the CVAE on several metrics, and QD+QVAE maintained gradability comparable to the full-data case.
C. Small Datasets
- The quarter-size training subset was randomly selected from the original RFMID dataset to test performance under smaller-data conditions.The paper frames small training and validation datasets as a constraint in many industrial generative-modeling applications.Source: C. Small Datasets · p. 7
- With classical diffusion on the quarter dataset, QVAE outperformed CVAE by larger margins than on the full dataset in FID, CMMD, and precision.The authors interpret this as evidence that QVAE captures image features better on smaller training sets, even though CVAE has more parameters.Source: C. Small Datasets · p. 7
- On the quarter dataset, QVAE outperformed all results in Automorph grading by at least 2−3×, while producing a percentage of gradable images comparable to the full RFMID case.Source: C. Small Datasets · p. 7
IV. CONCLUSION
The conclusion reports strong performance from the quantum-enhanced diffusion and VAE model for fundus image generation, while identifying hardware testing and broader applications as next steps.
IV. CONCLUSION
- QVAE+QDDPM performs best, producing the most gradable images and matching the real-image feature distribution most closely; simulated quantum noise increased image quality and diversity.On a reduced-size dataset, QVAE performed significantly better than CVAE in all metrics in CD runs.Source: §IV · p. 7
- Hardware sampling and training remain priorities for testing performance and realizing classically intractable model sizes and quantum speedups.The conclusion also points to quantum transfer learning as a possible aid to training quantum modules.Source: §IV · p. 7
- The authors identify 3D images, time series, and translation between imaging modalities as directions for extending quantum-enhanced diffusion models.Source: §IV · p. 7
- Flow matching is proposed as a natural quantum-enhanced direction because it can model arbitrary probability paths and has shown faster, smoother training than standard diffusion.Source: §IV · pp. 7–8
- Quantum variational algorithms face a scalability barrier from the trade-off between circuit expressivity and avoiding barren plateaus.Quantum reservoir computing is described as a barren-plateau-free approach that trains the classical output rather than quantum gate parameters.Source: §IV · p. 8
Appendix A: Diffusion Model
- The diffusion model learns image generation by adding Gaussian noise through a forward Markov process and learning its reverse to remove noise and generate images.The forward process approaches a standard normal distribution at large timestep counts; training minimizes the difference between true and predicted noise.Source: Appendix A · pp. 10–11
- The VAE encodes images into a compact Gaussian-normalized latent space for diffusion, then decodes that representation to reconstruct images.Its reconstruction loss combines pixel-wise loss, SSIM, and LPIPS.Source: Appendix A · p. 11
Appendix B: Full Ans¨atze
- ESE1 and ESE2 modify Strongly Entangling Layers to improve hardware efficiency for limited NISQ-device connectivity.ESE1 removes periodic boundaries; ESE2 also keeps i = 1 at each layer.Source: Appendix B · p. 11
Appendix C: Sampled Images
The sampled examples contrast image variety and feature clarity across four model types, with QD+QVAE images combining distinct features and higher variety than CD+QVAE.
Appendix C: Sampled Images
- QD+QVAE images combine distinct vessel features with higher variety than CD+QVAE images.The figure presents the first nine sampled Class 0 images from real data and four model types.Source: Appendix C · p. 11, Figure 5 · p. 12
- CDCNN+CVAE images show high variety but distortions that lead external validation to reject them as real images.Source: Appendix C · p. 11
- CD+QVAE images show distinct vessel segmentation and features but low variety, while QD+CVAE images have high variety but blurry features.Source: Appendix C · p. 11