[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84963-en":3,"doc-seo-84963-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},84963,7971461740886,"Theodore","https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2",8,"Research & Report","An Hybrid Quantum Classical Diffusion Model for Image Generation","Quantum diffusion models enable physics-consistent generative learning by performing noising and denoising directly on quantum states, yet classical high-dimensional data is limited by qubit-intensive state encoding and the heavy simulation cost of large density operators. A scalable hybrid pipeline is proposed: a classical autoencoder reduces dimension into compact latent codes embedded in a small-qubit Hilbert space, followed by an MSQuDDPM mixed-state quantum denoising diffusion model in latent space and decoding back to the image domain.","AN HYBRID QUANTUM-CLASSICAL DIFFUSION MODEL FOR IMAGE GENERATION  \nQipeng Qian 1 , Keli Deng2 , Yuntao Qian2  \n1 Program of Applied Mathematics, Department of Mathematics, University of Arizona, Tucson, USA  \n2 College of Computer Science and Technology, Zhejiang University, Hangzhou, China  \narXiv :2607 .07072v 1 [ cs .LG] 8 Jul 2026  \nABSTRACT  \nQuantum 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 asa practical backbone for hybrid quantum–classical generative modeling under realistic qubit budgets.  \nIndex Terms— Quantum diffusion model, Generation task  \n1. INTRODUCTION  \nDenoising diffusion probabilistic models (DDPMs) have become a central paradigm for modern generative modeling by learning a Markovian reverse process that progressively transforms simple noise into structured samples [1, 2] . This formulation has proved attractive in practice because it is stable to train and can achieve high sample quality, but it is also computationally demanding: sampling typically requires evaluating a denoiser across many timesteps, and the cost grows quickly with the dimensionality of the sample space.  \nMotivated by the search for more efficient generative mechanisms, quantum machine learning (QML) lever-  \nages variational quantum circuits and hybrid quantum– classical training, with recent work extending quantum models to structured data such as circuit-implementable quantum graph learning architectures (e.g., QSGCN [3] and quantum empowered GNNs for hyperspectral change detection [4]) . On the generative side, QGANs [5, 6] and hybrid variants have been explored for imaging tasks including hyperspectral restoration [7] and higherresolution synthesis [8], while diffusion-style quantum generators remain relatively scarce and largely confined to small-scale benchmarks [9] . A complementary direction therefore formulates diffusion directly over quantum states and channels, where forward noising and reverse denoising are physically valid CPTP maps and thereverse model preserves positivity and unit trace; QuDDPM [10] and its mixed-state extension MSQuDDPM [11] exemplify this approach by enabling generative learning over quantum ensembles while accounting for mixedness from decoherence, partial information, or stochastic preparation.  \nHowever, using quantum diffusion for classical generation faces a key bottleneck: encoding high-dimensional data (e.g. , images) quickly requires too many qubits, and density-matrix operations scale as 4N with the qubit number N. This limits expressive representations under practical simulation budgets. Inspired by latent diffusion, we mitigate this issue by learning in a compact latent space that can be embedded with only a small number of qubits.  \nIn this work, we propose a scalable hybrid pipeline that brings mixed-state quantum diffusion into classical generation by combining ","cbCaiubV1zCNq4Jk","https://ap.wps.com/l/cbCaiubV1zCNq4Jk","pdf",578488,3,1,7,"English","en",105,"# Abstract\n# Introduction\n## Background on DDPMs\n## Quantum diffusion and quantum generative models\n## Bottlenecks for classical generation\n## Proposed hybrid latent quantum diffusion pipeline\n## Key algorithmic contribution and contributions","[{\"question\":\"What problem do quantum diffusion models face when applied to classical high-dimensional data?\",\"answer\":\"They require qubit-heavy state encoding and incur high computational cost when simulating large density operators, which restricts practical expressive capacity under simulation budgets.\"},{\"question\":\"How does the proposed method make quantum diffusion scalable for image generation?\",\"answer\":\"It combines a classical autoencoder for dimensionality reduction with a mixed-state quantum denoising diffusion probabilistic model operating in the learned latent space, using a small-qubit embedding and decoding back to pixels.\"},{\"question\":\"What is the algorithmic change in the reverse diffusion step?\",\"answer\":\"Instead of learning an explicit predictor for ρ_{t−1}, the method predicts an estimate of the clean state ρ0 at timestep t and computes the one-step reverse update via an analytic backward propagation rule.\"}]",1784199739,18,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"an-hybrid-quantum-classical-diffusion-model-for-image-generation","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":20},"https://docshare.wps.com/document/research-report/",{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/an-hybrid-quantum-classical-diffusion-model-for-image-generation/84963/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-23","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What problem do quantum diffusion models face when applied to classical high-dimensional data?","Question",{"text":75,"@type":76},"They require qubit-heavy state encoding and incur high computational cost when simulating large density operators, which restricts practical expressive capacity under simulation budgets.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed method make quantum diffusion scalable for image generation?",{"text":80,"@type":76},"It combines a classical autoencoder for dimensionality reduction with a mixed-state quantum denoising diffusion probabilistic model operating in the learned latent space, using a small-qubit embedding and decoding back to pixels.",{"name":82,"@type":73,"acceptedAnswer":83},"What is the algorithmic change in the reverse diffusion step?",{"text":84,"@type":76},"Instead of learning an explicit predictor for ρ_{t−1}, the method predicts an estimate of the clean state ρ0 at timestep t and computes the one-step reverse update 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