{"url":"/method/lapgan","slug":"lapgan","name":"LAPGAN","full_name":"LAPGAN","full_name_withheld":false,"description_markdown":"A **LAPGAN**, or **Laplacian Generative Adversarial Network**, is a type of generative adversarial network that has a [Laplacian pyramid](https://paperswithcode.com/method/laplacian-pyramid) representation. In the sampling procedure following training, we have a set of generative convnet models {$G\\_{0}, \\dots , G\\_{K}$}, each of which captures the distribution of coefficients $h\\_{k}$ for natural images at a different level of the Laplacian pyramid. Sampling an image is akin to a reconstruction procedure, except that the generative\r\nmodels are used to produce the $h\\_{k}$’s:\r\n\r\n$$ \\tilde{I}\\_{k} = u\\left(\\tilde{I}\\_{k+1}\\right) + \\tilde{h}\\_{k} = u\\left(\\tilde{I}\\_{k+1}\\right) + G\\_{k}\\left(z\\_{k}, u\\left(\\tilde{I}\\_{k+1}\\right)\\right)$$\r\n\r\nThe recurrence starts by setting $\\tilde{I}\\_{K+1} = 0$ and using the model at the final level $G\\_{K}$ to generate a residual image $\\tilde{I}\\_{K}$ using noise vector $z\\_{K}$: $\\tilde{I}\\_{K} = G\\_{K}\\left(z\\_{K}\\right)$. Models at all levels except the final are conditional generative models that take an upsampled version of the current image $\\tilde{I}\\_{k+1}$ as a conditioning variable, in addition to the noise vector $z\\_{k}$.\r\n\r\nThe generative models {$G\\_{0}, \\dots, G\\_{K}$} are trained using the CGAN approach at each level of the pyramid. Specifically, we construct a Laplacian pyramid from each training image $I$. At each level we make a stochastic choice (with equal probability) to either (i) construct the coefficients $h\\_{k}$ either using the standard Laplacian pyramid coefficient generation procedure or (ii) generate them using $G\\_{k}:\r\n\r\n$$ \\tilde{h}\\_{k} = G\\_{k}\\left(z\\_{k}, u\\left(I\\_{k+1}\\right)\\right) $$\r\n\r\nHere $G\\_{k}$ is a convnet which uses a coarse scale version of the image $l\\_{k} = u\\left(I\\_{k+1}\\right)$ as an input, as well as noise vector $z\\_{k}$. $D\\_{k}$ takes as input $h\\_{k}$ or $\\tilde{h}\\_{k}$, along with the low-pass image $l\\_{k}$ (which is explicitly added to $h\\_{k}$ or $\\tilde{h}\\_{k}$ before the first [convolution](https://paperswithcode.com/method/convolution) layer), and predicts if the image was real or\r\ngenerated. At the final scale of the pyramid, the low frequency residual is sufficiently small that it\r\ncan be directly modeled with a standard [GAN](https://paperswithcode.com/method/gan): $\\tilde{h}\\_{K} = G\\_{K}\\left(z\\_{K}\\right)$ and $D\\_{K}$ only has $h\\_{K}$ or $\\tilde{h}\\_{K}$ as input.\r\n\r\nBreaking the generation into successive refinements is the key idea. We give up any “global” notion of fidelity; an attempt is never made to train a network to discriminate between the output of a cascade and a real image and instead the focus is on making each step plausible.","description_state":"present","introduced_year":null,"introduced_by":{"title":"Deep Generative Image Models using a Laplacian Pyramid of Adversarial Networks","paper":"/paper/deep-generative-image-models-using-a-1","first_author":"Emily Denton","n_authors":4,"url_abs":null,"archive_paper_url":"https://paperswithcode.com/paper/deep-generative-image-models-using-a-1"},"source":{"url":"http://arxiv.org/abs/1506.05751v1","title":"Deep Generative Image Models using a Laplacian Pyramid of Adversarial Networks","url_on_a_paper_host":true},"code_snippet_url":"https://github.com/AaronYALai/Generative_Adversarial_Networks_PyTorch/blob/master/LAPGAN/LAPGAN.py","code_snippet_url_on_a_code_host":true,"categories":[{"area":"Computer Vision","area_id":"computer-vision","collection":"Generative Adversarial Networks","url":"/methods/category/generative-adversarial-networks","pwc_aliases":[]},{"area":"Computer Vision","area_id":"computer-vision","collection":"Generative Models","url":"/methods/category/generative-models","pwc_aliases":[]}],"n_papers_tagged":5,"archive_num_papers":5,"papers_newest_first":[{"paper":null,"title":"Generative Adversarial Networks Bridging Art and Machine Intelligence","date":"2025-02-06","arxiv_id":"2502.04116","n_code_links":0,"syntology":null},{"paper":null,"title":"Medical Image Generation using Generative Adversarial Networks","date":"2020-05-19","arxiv_id":"2005.10687","n_code_links":0,"syntology":null},{"paper":null,"title":"Generating Highly Realistic Images of Skin Lesions with GANs","date":"2018-09-05","arxiv_id":"1809.01410","n_code_links":0,"syntology":null},{"paper":null,"title":"MelanoGANs: High Resolution Skin Lesion Synthesis with GANs","date":"2018-04-12","arxiv_id":"1804.04338","n_code_links":0,"syntology":null},{"paper":"/paper/deep-generative-image-models-using-a-1","title":"Deep Generative Image Models using a Laplacian Pyramid of Adversarial Networks","date":"2015-06-18","arxiv_id":"1506.05751","n_code_links":1,"syntology":null}],"papers_shown":5,"tasks":[{"task":"/task/image-generation","name":"Image Generation","papers":3},{"task":"/task/medical-image-analysis","name":"Medical Image Analysis","papers":2},{"task":"/task/machine-learning","name":"BIG-bench Machine Learning","papers":1},{"task":"/task/image-augmentation","name":"Image Augmentation","papers":1},{"task":"/task/image-reconstruction","name":"Image Reconstruction","papers":1},{"task":"/task/image-registration","name":"Image Registration","papers":1},{"task":"/task/image-to-image-translation","name":"Image-to-Image Translation","papers":1},{"task":"/task/lesion-classification","name":"Lesion Classification","papers":1},{"task":"/task/lesion-segmentation","name":"Lesion Segmentation","papers":1},{"task":"/task/medical-image-generation","name":"Medical Image Generation","papers":1},{"task":"/task/skin-lesion-classification","name":"Skin Lesion Classification","papers":1},{"task":"/task/skin-lesion-segmentation","name":"Skin Lesion Segmentation","papers":1},{"task":"/task/style-transfer","name":"Style Transfer","papers":1},{"task":"/task/text-to-image-generation-1","name":"Text to Image Generation","papers":1},{"task":"/task/text-to-image-generation","name":"Text-to-Image Generation","papers":1},{"task":"/task/translation","name":"Translation","papers":1},{"task":"/task/unsupervised-image-to-image-translation","name":"Unsupervised Image-To-Image Translation","papers":1},{"task":"/task/high","name":"Vocal Bursts Intensity Prediction","papers":1}],"tasks_shown":18,"n_tasks":18,"usage_by_year":[{"year":"2015","papers":1},{"year":"2018","papers":2},{"year":"2020","papers":1},{"year":"2025","papers":1}],"row_source":"methods_table","archive":{"source":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","archive_url":"https://paperswithcode.com/method/lapgan"},"syntology_read_at":"2026-09-24T18:15:14+00:00"}