Generative models have gained attention for their proven effectiveness in various domains, from generating images to producing text. Diffusion models (DMs) have demonstrated superior performance compared to alternative techniques like generative adversarial networks (GANs) or autoencoders (AE). The research about DMs has advanced further with the proposition of latent diffusion models (LDMs), which employ DMs within the latent space to mitigate computational complexity while preserving high quality and flexibility. Quantum computing with its intrinsic characteristics of entanglement and superposition which enable high representational power, arises with the possibility of offering computational advantages over classical generative models. Inspired by current trends of classical generative models, we propose quantum latent diffusion models (QLDMs) to enable computationally efficient DMs with the guidance of conditions on classical data. QLDMs offer solutions to the challenges faced by classical generative models due to their large number of parameters, while still achieving comparable results on datasets.
Generative models have gained attention for their proven effectiveness in various domains, from generating images to producing text. Diffusion models (DMs) have demonstrated superior performance compared to alternative techniques like generative adversarial networks (GANs) or autoencoders (AE). The research about DMs has advanced further with the proposition of latent diffusion models (LDMs), which employ DMs within the latent space to mitigate computational complexity while preserving high quality and flexibility. Quantum computing with its intrinsic characteristics of entanglement and superposition which enable high representational power, arises with the possibility of offering computational advantages over classical generative models. Inspired by current trends of classical generative models, we propose quantum latent diffusion models (QLDMs) to enable computationally efficient DMs with the guidance of conditions on classical data. QLDMs offer solutions to the challenges faced by classical generative models due to their large number of parameters, while still achieving comparable results on datasets.
Abstract Generative models realized with Machine Learning (ML) techniques are powerful tools to infer complex and unknown data distributions from a finite number of training samples in order to produce new synthetic data. Diffusion Models (DMs) are an emerging framework that have recently overcome Generative Adversarial Networks (GANs) in creating high‐quality images. Here, is proposed and discussed the quantum generalization of DMs, i.e., three Quantum‐Noise‐Driven Generative Diffusion Models (QNDGDMs) that could be experimentally tested on real quantum systems. The idea is to harness unique quantum features, in particular the non‐trivial interplay among coherence, entanglement, and noise that the currently available noisy quantum processors do unavoidably suffer from, in order to overcome the main computational burdens of classical diffusion models during inference. Hence, the suggestion is to exploit quantum noise not as an issue to be detected and solved but instead as a beneficial key ingredient to generate complex probability distributions from which a quantum processor might sample more efficiently than a classical one. Three examples of the numerical simulations are also included for the proposed approaches. The results are expected to pave the way for new quantum‐inspired or quantum‐based generative diffusion algorithms addressing tasks as data generation with widespread real‐world applications.
Quantum diffusion models are rapidly advancing generative remote-sensing analytics by harnessing quantum computation to deliver higher-quality, more realistic satellite images, while converging faster and with substantially fewer trainable parameters than comparable classical diffusers. In this context, we first realise a fully-quantum latent diffusion model (QLDM) whose denoiser is a variational-quantum circuit acting on a 10-dimensionaI latent code. On EuroSAT, focusing on three land-cover classes Forest, Herbaceous Vegetation and SeaLake, QLDM lowers the Fréchet Inception Distance (FID) and Kernel Inception Distance (KID) by 21.5 % and 29.9 %, respectively, relative to a parameter-matched classical latent diffuser. Yet the severe spatial compression intrinsic to latent processing limits fine-grained detail. To restore image fidelity, we develop a hybrid quantum—classical architecture—the Quanvolutional Conditioned U-Net (QCU-Net)—which inserts entangling quantum layers both at the U-Net bottleneck and as a quanvolutional filter early in the encoder. Trained on the full ten-class EuroSAT RGB set, QCU-Net reaches an FID of 2.57 and a KID of 0.0008, representing 64 % and 76 % improvements over the best classical diffusion baseline (FID = 7.22; KID = 0.0034), and boosts class-conditioning accuracy to 81.7 % versus 62.2 % for the classical model. Thèse gains confirm that embedding quantum circuits within the feature-extraction pipeline yields richer spatial— spectral representations than latent-space quantum processing alone. Our results outline a clear progression in quantum generative modelling for Earth Observation: by first demonstrating with the QLDM that fully quantum denoising is not only feasible but also highly parameter- efficient, then showing how the hybrid QCU-Net architecture restores perceptual fidelity by embedding quantum feature extractors within a classical U-Net backbone, and finally pointing toward a fully pixel-space quantum diffusion model as future work—one that would leverage deep quantum circuits to perform both the forward and reverse diffusion directly in Hilbert space, remove classical auto-encoding steps, and promise even greater image quality and efficiency on fault-tolerant hardware.
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 and 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 and experimental runs on hardware 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 noise.
Generative Artificial Intelligence is one of the most relevant technologies of our century, enabling digital machines not only to analyze or classify data but also to generate new content such as images, text, and video. This technology relies on deep learning algorithms designed to capture complex relationships from finite data sets. In this context, Diffusion Models have recently emerged as state-of-the-art in deep generative modeling thanks to their ability to produce high-quality data. Their pipeline typically consists of a forward diffusion process, where data samples are progressively corrupted into pure (classical) noise, and a reverse denoising process, where deep neural networks learn to reverse the diffusion process and then generate new synthetic samples. In parallel, Quantum Machine Learning represents one of the most promising applications of quantum computing. However, currently available quantum processors, known as Noisy Intermediate-Scale Quantum (NISQ) devices, are composed of tens or hundreds of noisy qubits. Therefore, designing scalable and efficient practical quantum algorithms represents a significant challenge. This thesis proposes the first generalization of classical Denoising Diffusion Probabilistic Models to the quantum domain, introducing the novel generative paradigm of Quantum Diffusion Models. In particular, the three possible scenarios are formalized and implemented: (i) classical data corrupted with Gaussian noise and a reverse process implemented via a quantum neural network; (ii) quantum data corrupted with quantum noise and a denoising process through a classical deep neural network; and (iii) a fully quantum approach, where both forward and backward processes are implemented within a quantum framework. Subsequently, the impact of different stochastic dynamics in the forward process is analyzed using the formalism of Quantum Stochastic Walks. We observe that a specific hybrid quantum-classical dynamics produces more statistically robust models, capable of generating sets of images closely resembling real ones compared to purely classical dynamics. Furthermore, we propose a hybrid quantum-classical diffusion model based on Quantum Walks that exploits the intrinsic noise of real quantum processors as a useful resource for generating images. This model is implementable on current NISQ devices and scalable, as it allows the generation of images of any size, requiring q + 1 qubits for grayscale images with pixel intensities in the range [0, 2^q - 1]. Finally, an application in the context of medical imaging is presented, specifically the generation of 64 × 64 color images of blood cells from the BloodMNIST dataset and 200 × 200 brain MRI images from the BraTS2020 dataset.
Deep generative models are key-enabling technology to computer vision, text generation, and large language models. Denoising diffusion probabilistic models (DDPMs) have recently gained much attention due to their ability to generate diverse and high-quality samples in many computer vision tasks, as well as to incorporate flexible model architectures and a relatively simple training scheme. Quantum generative models, empowered by entanglement and superposition, have brought new insight to learning classical and quantum data. Inspired by the classical counterpart, we propose the quantum denoising diffusion probabilistic model (QuDDPM) to enable efficiently trainable generative learning of quantum data. QuDDPM adopts sufficient layers of circuits to guarantee expressivity, while it introduces multiple intermediate training tasks as interpolation between the target distribution and noise to avoid barren plateau and guarantee efficient training. We provide bounds on the learning error and demonstrate QuDDPM's capability in learning correlated quantum noise model, quantum many-body phases, and topological structure of quantum data. The results provide a paradigm for versatile and efficient quantum generative learning.
Quantum diffusion models provide a physics-consistent route to generative learning by formulating noising and denoising directly on quantum states. However, applying such models to classical high-dimensional data is constrained by the qubit cost of state encoding and the computational burden of simulating large density operators. We propose a scalable hybrid generative pipeline that combines a classical autoencoder for dimensionality reduction with a mixed-state quantum denoising diffusion probabilistic model (MSQuDDPM) operating in the learned latent space. The autoencoder compresses data into compact latent codes that can be embedded into a small-qubit Hilbert space, after which the quantum diffusion model learns a generative distribution over latent density operators and decodes samples back to the original domain. Algorithmically, we simplify the reverse dynamics by predicting an estimate of the clean state ρ0 at timestep t and computing the one-step reverse update via an analytic backward propagation rule, rather than learning an explicit predictor for ρt−1. We demonstrate the proposed approach on MNIST image generation and discuss how mixed-state quantum diffusion can serve as a practical backbone for hybrid quantum--classical generative modeling under realistic qubit budgets.