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Quantum Generative Models for Image Generation: Insights from MNIST and MedMNIST

Chi-Sheng Chen, Wei An Hou, Hsiang-Wei Hu, Zhen-Sheng Cai

arXiv:2504.00034v2quant-phcs.LG

TL;DR

This study addresses the limited exploration of quantum diffusion for image generation by testing a hybrid quantum-classical model with a variational circuit in a lightweight U-Net bottleneck. It reports stronger performance in low-data MNIST settings and a mixed pattern on PathMNIST, alongside limitations in preserving local detail in complex color images.

  • Problem

    Research on quantum diffusion for image generation remains limited, motivating an exploratory test of whether quantum circuits can benefit image synthesis.

    Source: §I · p. 1, §II · p. 2

  • Method

    The study compares a hybrid quantum-classical diffusion model with a classical counterpart using the same lightweight U-Net architecture and a variational circuit in the bottleneck.

    Source: §I · p. 1

  • Results

    On MNIST with fewer than 100 training samples, the quantum model consistently outperformed its classical counterpart; on PathMNIST it had better FID but lower SSIM.

    Source: §V · p. 6

  • Takeaways & Limitations

    The study demonstrates the feasibility of training and evaluating quantum generators with classical feedback loops and provides a framework for standardized comparisons with classical diffusion models.

    Source: §V · p. 6

    The authors note that current quantum circuit designs may capture global distributional properties while struggling to preserve detailed local features in high-dimensional, color-rich image domains.

    Source: §V · p. 6

Abstract

from arXiv · show

Quantum generative models offer a promising new direction in machine learning by leveraging quantum circuits to enhance data generation capabilities. In this study, we propose a hybrid quantum-classical image generation framework that integrates variational quantum circuits into a diffusion-based model. To improve training dynamics and generation quality, we introduce two novel noise strategies: intrinsic quantum-generated noise and a tailored noise scheduling mechanism. Our method is built upon a lightweight U-Net architecture, with the quantum layer embedded in the bottleneck module to isolate its effect. We evaluate our model on MNIST and MedMNIST datasets to examine its feasibility and performance. Notably, our results reveal that under limited data conditions (fewer than 100 training images), the quantum-enhanced model generates images with higher perceptual quality and distributional similarity than its classical counterpart using the same architecture. While the quantum model shows advantages on grayscale data such as MNIST, its performance is more nuanced on complex, color-rich datasets like PathMNIST. These findings highlight both the potential and current limitations of quantum generative models and lay the groundwork for future developments in low-resource and biomedical image generation.

I. INTRODUCTION

Classical generative models face computational and scalability challenges as data complexity grows, while quantum diffusion remains an exploratory direction with limited research. This work tests a hybrid quantum-classical diffusion model against an architecture-matched classical baseline on MNIST and MedMNIST.

I. INTRODUCTION

  • Classical generative models face increasing computational and scalability challenges as data complexity rises.Source: §I · p. 1
  • Quantum circuits and diffusion models are presented as a promising direction for image synthesis, with PQCs proposed as compact representations of complex distributions.Source: §I · p. 1
  • The study tests whether adding a quantum layer improves generation quality over a classical diffusion model with the same architecture, using MNIST and MedMNIST.The lightweight U-Net keeps its encoder and decoder unchanged while replacing the classical bottleneck with a variational quantum circuit.Source: §I · p. 1

II. RELATED WORK

  • Prior work covers QGANs, quantum VAEs, circuit Born machines, and quantum approaches to biomedical imaging, including MedMNIST classification.Source: §II · pp. 1–2
  • The authors identify limited research on quantum diffusion for image generation and frame their study as an exploratory investigation of possible image-synthesis benefits.Source: §II · p. 2

III. METHODOLOGY

The method compares a hybrid quantum-classical diffusion model with a classical model using the same simplified U-Net structure and training procedures. The quantum circuit is incorporated in the bottleneck, with experiments on class-conditional MNIST subsets.

A. Overview

  • The proposed model is a hybrid quantum-classical diffusion model built on a simplified U-Net with an optional variational quantum attention layer.Source: A. Overview · p. 2
  • Figure 1 presents the model architecture of the quantum diffusion model.Source: Figure 1 · p. 2
  • Both models use the same structure and training procedures, enabling comparison of a parameterized quantum circuit in the diffusion U-Net bottleneck.Source: A. Overview · p. 2

B. Diffusion Process

The diffusion process progressively adds Gaussian noise to images, using a cosine schedule for the noise parameters. The denoising model is trained to predict the noise added at each timestep.

B. Diffusion Process

C. Improved U-Net Architecture and Timestep Embedding

The denoiser is a lightweight U-Net conditioned on diffusion timestep embeddings. Its quantum-enhanced version inserts a variational quantum layer in the bottleneck, transforms pooled features through a circuit, and integrates the output back into the feature map.

C. Improved U-Net Architecture and Timestep Embedding

D. Quantum Layer

  • The quantum layer applies global average pooling to the bottleneck feature map, then projects the resulting 128-dimensional latent vector to 16 dimensions for the circuit.Source: D. Quantum Layer · p. 3
  • The 16-dimensional input is encoded on 16 qubits, processed by three variational layers with trainable RZ gates and linear CNOT entanglement, and read out as Pauli-Z expectation values.Source: D. Quantum Layer · p. 3
  • A fully connected layer maps the quantum output back to 128 dimensions for elementwise multiplication with the original bottleneck feature map.Source: D. Quantum Layer · p. 3
  • The quantum module is implemented as a differentiable PennyLane QNode and trained end-to-end with gradient-based optimization using the parameter-shift rule.Source: D. Quantum Layer · p. 3

E. Training Strategy and EMA

Training uses noisy images at randomly sampled timesteps, with the model learning to predict the added noise. EMA stabilizes the parameters used to generate and evaluate samples.

E. Training Strategy and EMA

  • The model predicts added Gaussian noise for a randomly sampled timestep and is optimized with mean squared error using Adam at a learning rate of 3 × 10−4.Training is performed on individual classes from MNIST and MedMNIST.Source: E. Training Strategy and EMA · p. 3
  • EMA parameters are updated with β = 0.999 to stabilize training and improve sample quality.Source: E. Training Strategy and EMA · p. 3
  • After each epoch, the EMA model generates samples for visual inspection, and the best-performing model is retained for inference.Source: E. Training Strategy and EMA · p. 3

A. Datasets and Experimental Setup

Experiments use MNIST and a 2D MedMNIST subset, PathMNIST, with original-resolution images. Both datasets share a 30-epoch training setup.

A. Datasets and Experimental Setup

  • MNIST uses 28 × 28 grayscale images and a training subset such as digits 0 and 1, while PathMNIST provides a more complex biomedical image test case.MNIST has 60,000 training and 10,000 test samples; the model is in principle capable of handling all digits with sufficient capacity.Source: A. Datasets and Experimental Setup · p. 3
  • Images are processed at original resolution without downsampling, dimensionality reduction, padding, interpolation, or resizing; MNIST is single-channel and PathMNIST retains independently normalized RGB channels.Source: A. Datasets and Experimental Setup · p. 3
  • Both datasets use 30 epochs, batch size 64, and Adam with learning rate 3 × 10−4; quantum computation is simulator-based and supports end-to-end differentiation in one forward pass.The quantum attention module operates on the bottleneck representation.Source: A. Datasets and Experimental Setup · pp. 3–4

B. Evaluation Metrics

The evaluation combines perceptual and distributional similarity metrics with the diffusion model’s denoising objective. The supplied figure caption identifies a classical-versus-quantum image comparison for MNIST digit 0.

B. Evaluation Metrics

  • FID compares Gaussian feature distributions of real and generated images, with lower FID indicating closer distributional similarity.Source: B. Evaluation Metrics · p. 4
  • SSIM assesses perceptual quality between generated and reference real images using their means, variances, and covariance.Source: B. Evaluation Metrics · p. 4
  • The diffusion generator is trained to estimate added noise at each timestep, using mean squared error between predicted and true noise rather than classification accuracy.The noisy input combines the original sample with Gaussian noise, and the model is trained to reverse that forward process.Source: B. Evaluation Metrics · p. 4
  • Samples for visualization and evaluation are generated using the exponential-moving-average model after each epoch.Source: B. Evaluation Metrics · p. 4
  • Figure 3 compares classical and quantum diffusion-model images for MNIST digit 0.Source: Figure 3 · p. 4

C. Results on MNIST

On MNIST, the quantum model scored higher on average SSIM and lower on average FID than the classical baseline, with variability differing across metrics.

C. Results on MNIST

  • The MNIST comparison covers all digit classes after 30 training epochs and reports SSIM and FID averages and standard deviations.Table I summarizes scores across digits 0–9.Source: C. Results on MNIST · p. 4
  • The authors report that quantum components may enhance generated-image fidelity and perceptual quality, particularly for fine-grained structural details.SSIM reflects perceptual image quality, with higher values better; FID assesses distributional similarity, with lower values better.Source: C. Results on MNIST · p. 4
  • SSIM averaged 0.1263 for the quantum model versus 0.1085 for the classical model, while quantum SSIM standard deviation was 0.0477.The quantum model scored higher on several digits, including digit 4 (0.2000 vs. 0.1119) and digit 6 (0.2052 vs. 0.1238).Source: C. Results on MNIST · p. 4, Table I · p. 5
  • FID averaged 259.25 for the quantum model versus 271.05 for the classical model, and its FID standard deviation was 33.04 versus 38.18.The lower average FID indicates better alignment between generated and real image distributions, while the lower standard deviation indicates more consistent performance.Source: C. Results on MNIST · p. 4, Table I · p. 5

D. Results on MedMNIST

On PathMNIST, the classical model scored higher on SSIM, while the quantum model scored better on FID; the authors describe the results as a nuanced trade-off.

D. Results on MedMNIST

  • The PathMNIST comparison evaluates images generated after 30 epochs and is described as a trade-off between SSIM and FID.PathMNIST is characterized as more complex and color-rich than MNIST.Source: D. Results on MedMNIST · p. 5, Figure 7 · p. 6
  • SSIM was 0.4107 for the classical model versus 0.0931 for the quantum model on PathMNIST.The authors say the classical model better preserved structural similarity in the generated color images.Source: D. Results on MedMNIST · p. 5
  • FID was 84.40 for the quantum model versus 95.72 for the classical model on PathMNIST.The authors describe the quantum model as better matching the global distribution of real images, while individual-image quality and perceptual similarity may be less satisfactory.Source: D. Results on MedMNIST · p. 5
  • The authors caution that benefits observed on grayscale MNIST may not transfer directly to complex, color-based PathMNIST.They suggest improving quantum architectures to better handle color information and spatial complexity.Source: D. Results on MedMNIST · p. 5

V. DISCUSSION AND CONCLUSION

The quantum model outperformed its same-architecture classical counterpart with fewer than 100 training images, but its PathMNIST results show a trade-off between global distribution alignment and fine-grained fidelity. The study also demonstrates a practical framework for biomedical image generation and identifies directions for further development.

V. DISCUSSION AND CONCLUSION

  • Fewer than 100 training images yielded consistent quantum-model outperformance over the same-architecture classical counterpart, while PathMNIST showed better FID but significantly lower SSIM.The PathMNIST SSIM result reflects weaker fine-grained spatial fidelity in generated images.Source: §V · p. 6
  • The discrepancy suggests quantum models may capture global distributional properties yet struggle with detailed local features in high-dimensional, color-rich image domains.The authors suggest current circuit designs may suit abstract or low-dimensional representations better than detailed spatial structures.Source: §V · p. 6
  • The study presents an early biomedical-image application and demonstrates training and evaluation with classical feedback loops under standardized metrics.Source: §V · p. 6
  • Future work should explore more expressive circuits, higher qubit counts, hybrid feature-extraction strategies, alternative generative paradigms, and real-hardware evaluation.Source: §V · p. 6
  • The authors anticipate hybrid quantum-classical generation could become relevant to efficient, compact, interpretable synthesis, including low-resource medical imaging.Source: §V · p. 6
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