{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T11:17:38Z","timestamp":1775215058621,"version":"3.50.1"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"12","license":[{"start":{"date-parts":[[2023,6,2]],"date-time":"2023-06-02T00:00:00Z","timestamp":1685664000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,6,2]],"date-time":"2023-06-02T00:00:00Z","timestamp":1685664000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Alma Mater Studiorum - Universit\u00e0 di Bologna"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Artif Intell Rev"],"published-print":{"date-parts":[[2023,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Denoising Diffusion models are gaining increasing popularity in the field of generative modeling for several reasons, including the simple and stable training, the excellent generative quality, and the solid probabilistic foundation. In this article, we address the problem of <jats:italic>embedding<\/jats:italic> an image into the latent space of Denoising Diffusion Models, that is finding a suitable \u201cnoisy\u201d image whose denoising results in the original image. We particularly focus on Denoising Diffusion Implicit Models due to the deterministic nature of their reverse diffusion process. As a side result of our investigation, we gain a deeper insight into the structure of the latent space of diffusion models, opening interesting perspectives on its exploration, the definition of semantic trajectories, and the manipulation\/conditioning of encodings for editing purposes. A particularly interesting property highlighted by our research, which is also characteristic of this class of generative models, is the independence of the latent representation from the networks implementing the reverse diffusion process. In other words, a common seed passed to different networks (each trained on the same dataset), eventually results in identical images.<\/jats:p>","DOI":"10.1007\/s10462-023-10504-5","type":"journal-article","created":{"date-parts":[[2023,6,2]],"date-time":"2023-06-02T18:02:10Z","timestamp":1685728930000},"page":"14511-14533","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Image embedding for denoising generative models"],"prefix":"10.1007","volume":"56","author":[{"given":"Andrea","family":"Asperti","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Davide","family":"Evangelista","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Samuele","family":"Marro","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fabio","family":"Merizzi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,6,2]]},"reference":[{"key":"10504_CR1","doi-asserted-by":"publisher","unstructured":"Abdal R, Qin Y, Wonka P (2019) Image2stylegan: How to embed images into the stylegan latent space? In: 2019 IEEE\/CVF international conference on computer vision, ICCV 2019, Seoul, Korea (South), October 27 - November 2, 2019, IEEE, pp 4431\u20134440. https:\/\/doi.org\/10.1109\/ICCV.2019.00453","DOI":"10.1109\/ICCV.2019.00453"},{"key":"10504_CR2","doi-asserted-by":"crossref","unstructured":"Abdal R, Qin Y, Wonka P (2020) Image2stylegan++: How to edit the embedded images? In: Proceedings of the IEEE\/CVF conference on computer vision and pattern recognition, pp 8296\u20138305","DOI":"10.1109\/CVPR42600.2020.00832"},{"key":"10504_CR3","doi-asserted-by":"crossref","unstructured":"Alaluf Y, Tov O, Mokady R, Gal R, Bermano A (2022) Hyperstyle: Stylegan inversion with hypernetworks for real image editing. In: Proceedings of the IEEE\/CVF conference on computer vision and pattern recognition, pp 18511\u201318521","DOI":"10.1109\/CVPR52688.2022.01796"},{"issue":"10","key":"10504_CR4","doi-asserted-by":"publisher","first-page":"2459","DOI":"10.1007\/s11263-020-01310-5","volume":"128","author":"R Anirudh","year":"2020","unstructured":"Anirudh R, Thiagarajan JJ, Kailkhura B, Bremer PT (2020) Mimicgan: Robust projection onto image manifolds with corruption mimicking. Int J Comput Vis 128(10):2459\u20132477","journal-title":"Int J Comput Vis"},{"issue":"4","key":"10504_CR5","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1007\/s42979-021-00702-9","volume":"2","author":"A Asperti","year":"2021","unstructured":"Asperti A, Evangelista D, Piccolomini EL (2021) A survey on variational autoencoders from a green AI perspective. SN Comput Sci 2(4):301. https:\/\/doi.org\/10.1007\/s42979-021-00702-9","journal-title":"SN Comput Sci"},{"key":"10504_CR6","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-022-07890-2","author":"A Asperti","year":"2022","unstructured":"Asperti A, Tonelli V (2022) Comparing the latent space of generative models. Neural Comput Appl. https:\/\/doi.org\/10.1007\/s00521-022-07890-2","journal-title":"Neural Comput Appl"},{"issue":"4","key":"10504_CR7","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1145\/3306346.3323023","volume":"38","author":"D Bau","year":"2019","unstructured":"Bau D, Strobelt H, Peebles WS, Wulff J, Zhou B, Zhu J, Torralba A (2019) Semantic photo manipulation with a generative image prior. ACM Trans Graph 38(4):59\u201315911","journal-title":"ACM Trans Graph"},{"key":"10504_CR8","doi-asserted-by":"crossref","unstructured":"Chen L, Chu X, Zhang X, Sun J (2022) Simple baselines for image restoration. In: Computer Vision\u2013ECCV 2022: 17th European conference, Tel Aviv, Israel, October 23\u201327, 2022, Proceedings, Part VII, Springer, pp 17\u201333","DOI":"10.1007\/978-3-031-20071-7_2"},{"key":"10504_CR9","doi-asserted-by":"publisher","unstructured":"Choi J, Kim S, Jeong Y, Gwon Y, Yoon S (2021) ILVR: conditioning method for denoising diffusion probabilistic models. In: 2021 IEEE\/CVF International conference on computer vision, ICCV 2021, Montreal, QC, Canada, October 10-17, 2021, pp 14347\u201314356. https:\/\/doi.org\/10.1109\/ICCV48922.2021.01410","DOI":"10.1109\/ICCV48922.2021.01410"},{"key":"10504_CR10","doi-asserted-by":"crossref","unstructured":"Collins E, Bala R, Price B, Susstrunk S (2020) Editing in style: Uncovering the local semantics of gans. In: Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, pp 5771\u20135780","DOI":"10.1109\/CVPR42600.2020.00581"},{"issue":"7","key":"10504_CR11","doi-asserted-by":"publisher","first-page":"1967","DOI":"10.1109\/TNNLS.2018.2875194","volume":"30","author":"A Creswell","year":"2019","unstructured":"Creswell A, Bharath AA (2019) Inverting the generator of a generative adversarial network. IEEE Trans Neural Networks Learn Syst 30(7):1967\u20131974","journal-title":"IEEE Trans Neural Networks Learn Syst"},{"key":"10504_CR12","doi-asserted-by":"crossref","unstructured":"Daras G, Odena A, Zhang H, Dimakis AG (2020) Your local gan: designing two dimensional local attention mechanisms for generative models. In: Proceedings of the IEEE\/CVF conference on computer vision and pattern recognition, pp 14531\u201314539","DOI":"10.1109\/CVPR42600.2020.01454"},{"key":"10504_CR13","unstructured":"Dhariwal P, Nichol AQ (2021) Diffusion models beat gans on image synthesis. In: Ranzato M, Beygelzimer A, Dauphin YN, Liang P, Vaughan JW (eds) Advances in neural information processing systems 34: annual conference on neural information processing systems 2021, NeurIPS 2021, December 6-14, 2021, Virtual, pp 8780\u20138794 . https:\/\/proceedings.neurips.cc\/paper\/2021\/hash\/49ad23d1ec9fa4bd8d77d02681df5cfa-Abstract.html"},{"key":"10504_CR14","unstructured":"Dong Z, Wei P, Lin L (2022) Dreamartist: Towards controllable one-shot text-to-image generation via contrastive prompt-tuning. arxiv:2211.11337"},{"key":"10504_CR15","unstructured":"Gal R, Alaluf Y, Atzmon Y, Patashnik O, Bermano AH, Chechik G, Cohen-Or D (2022) An image is worth one word: Personalizing text-to-image generation using textual inversion. arxiv:2208.01618"},{"key":"10504_CR16","unstructured":"Ho J, Jain A, Abbeel P (2020) Denoising diffusion probabilistic models. In: Larochelle H, Ranzato M, Hadsell R, Balcan M, Lin H (eds) Advances in neural information processing systems 33: annual conference on neural information processing systems 2020, NeurIPS 2020, December 6-12, 2020, Virtual. https:\/\/proceedings.neurips.cc\/paper\/2020\/hash\/4c5bcfec8584af0d967f1ab10179ca4b-Abstract.html"},{"key":"10504_CR17","unstructured":"Ho J, Salimans T, Gritsenko A, Chan W, Norouzi M, Fleet DJ (2022) Video diffusion models. arXiv: 2204.03458"},{"issue":"8","key":"10504_CR18","doi-asserted-by":"publisher","first-page":"2011","DOI":"10.1109\/TPAMI.2019.2913372","volume":"42","author":"J Hu","year":"2020","unstructured":"Hu J, Shen L, Albanie S, Sun G, Wu E (2020) Squeeze-and-excitation networks. IEEE Trans Pattern Anal Mach Intell 42(8):2011\u20132023. https:\/\/doi.org\/10.1109\/TPAMI.2019.2913372","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"10504_CR19","first-page":"852","volume":"34","author":"T Karras","year":"2021","unstructured":"Karras T, Aittala M, Laine S, H\u00e4rk\u00f6nen E, Hellsten J, Lehtinen J, Aila T (2021) Alias-free generative adversarial networks. Adv Neural Inf Process Syst 34:852\u2013863","journal-title":"Adv Neural Inf Process Syst"},{"key":"10504_CR20","doi-asserted-by":"crossref","unstructured":"Karras T, Laine S, Aila T (2019) A style-based generator architecture for generative adversarial networks. In: Proceedings of the IEEE\/CVF conference on computer vision and pattern recognition, pp 4401\u20134410","DOI":"10.1109\/CVPR.2019.00453"},{"key":"10504_CR21","doi-asserted-by":"crossref","unstructured":"Karras T, Laine S, Aittala M, Hellsten J, Lehtinen J, Aila T (2020) Analyzing and improving the image quality of stylegan. In: Proceedings of the IEEE\/CVF conference on computer vision and pattern recognition, pp 8110\u20138119","DOI":"10.1109\/CVPR42600.2020.00813"},{"key":"10504_CR22","unstructured":"Khrulkov V, Oseledets I (2022) Understanding ddpm latent codes through optimal transport. arxiv:2202.07477"},{"key":"10504_CR23","first-page":"21696","volume":"34","author":"D Kingma","year":"2021","unstructured":"Kingma D, Salimans T, Poole B, Ho J (2021) Variational diffusion models. Adv Neural Inf Process Syst 34:21696\u201321707","journal-title":"Adv Neural Inf Process Syst"},{"issue":"4","key":"10504_CR24","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1561\/2200000056","volume":"12","author":"DP Kingma","year":"2019","unstructured":"Kingma DP, Welling M (2019) An introduction to variational autoencoders. Found Trends Mach Learn 12(4):307\u2013392. https:\/\/doi.org\/10.1561\/2200000056","journal-title":"Found Trends Mach Learn"},{"key":"10504_CR25","doi-asserted-by":"publisher","unstructured":"Kwon M, Jeong J, Uh Y (2022) Diffusion models already have a semantic latent space. CoRR arxiv:2210.10960, https:\/\/doi.org\/10.48550\/arXiv.2210.10960","DOI":"10.48550\/arXiv.2210.10960"},{"issue":"1","key":"10504_CR26","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1109\/TAI.2021.3071642","volume":"2","author":"Z Li","year":"2021","unstructured":"Li Z, Tao R, Wang J, Li F, Niu H, Yue M, Li B (2021) Interpreting the latent space of gans via measuring decoupling. IEEE Trans Artif Intell 2(1):58\u201370","journal-title":"IEEE Trans Artif Intell"},{"key":"10504_CR27","doi-asserted-by":"crossref","unstructured":"Li G, Liu Y, Wei X, Zhang Y, Wu S, Xu Y, Wong HS (2021) Discovering density-preserving latent space walks in gans for semantic image transformations. In: Proceedings of the 29th ACM international conference on multimedia, pp 1562\u20131570","DOI":"10.1145\/3474085.3475293"},{"key":"10504_CR28","doi-asserted-by":"crossref","unstructured":"Liu Z, Luo P, Wang X, Tang X (2015) Deep learning face attributes in the wild. In: Proceedings of International Conference on Computer Vision (ICCV), pp 3730\u20133738","DOI":"10.1109\/ICCV.2015.425"},{"key":"10504_CR29","unstructured":"Nichol AQ, Dhariwal P (2021) Improved denoising diffusion probabilistic models. In: International conference on machine learning, PMLR, pp 8162\u20138171"},{"key":"10504_CR30","unstructured":"Perarnau G, Van De\u00a0Weijer J, Raducanu B, \u00c1lvarez JM (2016) Invertible conditional gans for image editing. arXiv preprint arXiv:1611.06355"},{"key":"10504_CR31","unstructured":"Poirier-Ginter Y, Lessard A, Smith R, Lalonde JF (2022) Overparameterization improves stylegan inversion. arxiv:2205.06304"},{"key":"10504_CR32","unstructured":"Ramesh A, Dhariwal P, Nichol A, Chu C, Chen M (2022) Hierarchical text-conditional image generation with CLIP latents. arXiv. arxiv:2204.06125"},{"key":"10504_CR33","doi-asserted-by":"crossref","unstructured":"Ronneberger O, Fischer P, Brox T (2015) U-net: Convolutional networks for biomedical image segmentation. In: International conference on medical image computing and computer-assisted intervention, Springer pp 234\u2013241","DOI":"10.1007\/978-3-319-24574-4_28"},{"key":"10504_CR34","doi-asserted-by":"publisher","unstructured":"Saharia C, Chan W, Saxena S, Li L, Whang J, Denton E, Ghasemipour SKS, Ayan BK, Mahdavi SS, Lopes RG, Salimans T, Ho J, Fleet DJ, Norouzi M (2022) Photorealistic text-to-image diffusion models with deep language understanding. CoRR arxiv: 2205.11487, https:\/\/doi.org\/10.48550\/arXiv.2205.11487","DOI":"10.48550\/arXiv.2205.11487"},{"issue":"4","key":"10504_CR35","doi-asserted-by":"publisher","first-page":"2004","DOI":"10.1109\/TPAMI.2020.3034267","volume":"44","author":"Y Shen","year":"2022","unstructured":"Shen Y, Yang C, Tang X, Zhou B (2022) Interfacegan: interpreting the disentangled face representation learned by gans. IEEE Trans Pattern Anal Mach Intell 44(4):2004\u20132018. https:\/\/doi.org\/10.1109\/TPAMI.2020.3034267","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"key":"10504_CR36","unstructured":"Song Y, Sohl-Dickstein J, Kingma DP, Kumar A, Ermon S, Poole B (2020) Score-based generative modeling through stochastic differential equations. arxiv:2011.13456"},{"key":"10504_CR37","unstructured":"Song J, Meng C, Ermon S (2021) Denoising diffusion implicit models. In: 9th International Conference on Learning Representations, ICLR 2021, Virtual Event, Austria, May 3-7, 2021. OpenReview.net, ??? . https:\/\/openreview.net\/forum?id=St1giarCHLP"},{"key":"10504_CR38","unstructured":"Vaswani A, Shazeer N, Parmar N, Uszkoreit J, Jones L, Gomez AN, Kaiser L, Polosukhin I (2017) Attention is all you need. In: advances in neural information processing systems 30: Annual conference on neural information processing systems 2017, December 4-9, 2017, Long Beach, CA, USA, pp 5998\u20136008 . https:\/\/proceedings.neurips.cc\/paper\/2017\/hash\/3f5ee243547dee91fbd053c1c4a845aa-Abstract.html"},{"key":"10504_CR39","doi-asserted-by":"crossref","unstructured":"Xia W, Zhang Y, Yang Y, Xue JH, Zhou B, Yang MH (2022) Gan inversion: a survey. In: IEEE transactions on pattern analysis and machine intelligence","DOI":"10.1109\/TPAMI.2022.3181070"},{"key":"10504_CR40","doi-asserted-by":"publisher","unstructured":"Zhu J, Kr\u00e4henb\u00fchl P, Shechtman E, Efros AA (2016) Generative visual manipulation on the natural image manifold. In: Computer Vision - ECCV 2016 - 14th European conference, Amsterdam, The Netherlands, October 11-14, 2016, Proceedings, Part V. Lecture notes in computer science, vol 9909. Springer, pp 597\u2013613.https:\/\/doi.org\/10.1007\/978-3-319-46454-1_36","DOI":"10.1007\/978-3-319-46454-1_36"},{"key":"10504_CR41","doi-asserted-by":"publisher","unstructured":"Zhu J, Shen Y, Zhao D, Zhou B (2020) In-domain GAN inversion for real image editing. In: Computer Vision - ECCV 2020 - 16th European conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part XVII. Lecture notes in computer science, vol 12362. Springer, pp 592\u2013608. https:\/\/doi.org\/10.1007\/978-3-030-58520-4_35","DOI":"10.1007\/978-3-030-58520-4_35"}],"container-title":["Artificial Intelligence Review"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10462-023-10504-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10462-023-10504-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10462-023-10504-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,5]],"date-time":"2023-10-05T10:24:25Z","timestamp":1696501465000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10462-023-10504-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,2]]},"references-count":41,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2023,12]]}},"alternative-id":["10504"],"URL":"https:\/\/doi.org\/10.1007\/s10462-023-10504-5","relation":{},"ISSN":["0269-2821","1573-7462"],"issn-type":[{"value":"0269-2821","type":"print"},{"value":"1573-7462","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,6,2]]},"assertion":[{"value":"2 June 2023","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"On behalf of all authors, the corresponding author states that there is no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}