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Specifically, we propose two possible different hybridization schemes combining quantum computing\u2019s superior generalization with classical networks\u2019 modularity. In the first one, we acted at the vertex: ResNet convolutional layers are gradually replaced with variational circuits to create Quantum ResNet blocks. In the second proposed architecture, we extend the hybridization to the intermediate level of the encoder, due to its higher sensitivity in the feature extraction process. In order to conduct an in-depth analysis of the potential advantages stemming from the integration of quantum layers, images generated by quantum hybrid diffusion models are compared to those generated by classical models, and evaluated in terms of several quantitative metrics. The results demonstrate an advantage in using hybrid quantum diffusion models, as they generally synthesize better-quality images and converges faster. Moreover, they show the additional advantage of having a lower number of parameters to train compared to the classical one, with a reduction that depends on the extent to which the vertex is hybridized.<\/jats:p>","DOI":"10.1007\/s13218-024-00858-5","type":"journal-article","created":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T14:02:52Z","timestamp":1723212172000},"page":"311-326","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Quantum Hybrid Diffusion Models for Image Synthesis"],"prefix":"10.1007","volume":"38","author":[{"given":"Francesca","family":"De Falco","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andrea","family":"Ceschini","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alessandro","family":"Sebastianelli","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bertrand","family":"Le Saux","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9876-1494","authenticated-orcid":false,"given":"Massimo","family":"Panella","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,8,9]]},"reference":[{"key":"858_CR1","unstructured":"Farhi E, Neven H (2018) Classification with quantum neural networks on near term processors. arXiv: QuantumPhysics (2018). https:\/\/api.semanticscholar.org\/CorpusID:119037649"},{"key":"858_CR2","doi-asserted-by":"crossref","unstructured":"Johri S, Debnath S, Mocherla A, Singh A, Prakash A, Kim J, Kerenidis I (2021) Nearest centroid classification on a trapped ion quantum computer. npj Quantum Inf. https:\/\/hal.science\/hal-03432449","DOI":"10.1038\/s41534-021-00456-5"},{"issue":"6","key":"858_CR3","doi-asserted-by":"publisher","first-page":"60002","DOI":"10.1209\/0295-5075\/119\/60002","volume":"119","author":"M Schuld","year":"2017","unstructured":"Schuld M, Fingerhuth M, Petruccione F (2017) Implementing a distance-based classifier with a quantum interference circuit. 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