{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,30]],"date-time":"2026-06-30T17:47:07Z","timestamp":1782841627812,"version":"3.54.5"},"reference-count":94,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,10,20]],"date-time":"2023-10-20T00:00:00Z","timestamp":1697760000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"IARPA WRIVA program","award":["2047418"],"award-info":[{"award-number":["2047418"]}]},{"name":"IARPA WRIVA program","award":["2003237"],"award-info":[{"award-number":["2003237"]}]},{"name":"IARPA WRIVA program","award":["2007719"],"award-info":[{"award-number":["2007719"]}]},{"name":"IARPA WRIVA program","award":["DE-SC0022331"],"award-info":[{"award-number":["DE-SC0022331"]}]},{"name":"Department of Energy, Office of Science","award":["2047418"],"award-info":[{"award-number":["2047418"]}]},{"name":"Department of Energy, Office of Science","award":["2003237"],"award-info":[{"award-number":["2003237"]}]},{"name":"Department of Energy, Office of Science","award":["2007719"],"award-info":[{"award-number":["2007719"]}]},{"name":"Department of Energy, Office of Science","award":["DE-SC0022331"],"award-info":[{"award-number":["DE-SC0022331"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Denoising diffusion probabilistic models are a promising new class of generative models that mark a milestone in high-quality image generation. This paper showcases their ability to sequentially generate video, surpassing prior methods in perceptual and probabilistic forecasting metrics. We propose an autoregressive, end-to-end optimized video diffusion model inspired by recent advances in neural video compression. The model successively generates future frames by correcting a deterministic next-frame prediction using a stochastic residual generated by an inverse diffusion process. We compare this approach against six baselines on four datasets involving natural and simulation-based videos. We find significant improvements in terms of perceptual quality and probabilistic frame forecasting ability for all datasets.<\/jats:p>","DOI":"10.3390\/e25101469","type":"journal-article","created":{"date-parts":[[2023,10,20]],"date-time":"2023-10-20T11:53:56Z","timestamp":1697802836000},"page":"1469","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":129,"title":["Diffusion Probabilistic Modeling for Video Generation"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3154-4150","authenticated-orcid":false,"given":"Ruihan","family":"Yang","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of California, Irvine, CA 92697, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Prakhar","family":"Srivastava","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of California, Irvine, CA 92697, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7836-7839","authenticated-orcid":false,"given":"Stephan","family":"Mandt","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of California, Irvine, CA 92697, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2806","DOI":"10.1109\/TPAMI.2020.3045007","article-title":"A review on deep learning techniques for video prediction","volume":"44","author":"Oprea","year":"2020","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_2","unstructured":"Vondrick, C., Pirsiavash, H., and Torralba, A. (July, January 26). Anticipating visual representations from unlabeled video. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Las Vegas, NV, USA."},{"key":"ref_3","unstructured":"Ha, D., and Schmidhuber, J. (2018). World models. arXiv."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Liu, Z., Yeh, R.A., Tang, X., Liu, Y., and Agarwala, A. (2017, January 22\u201329). Video frame synthesis using deep voxel flow. Proceedings of the IEEE International Conference on Computer Vision, Venice, Italy.","DOI":"10.1109\/ICCV.2017.478"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Bhattacharyya, A., Fritz, M., and Schiele, B. (2018, January 18\u201322). Long-term on-board prediction of people in traffic scenes under uncertainty. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Salt Lake City, UT, USA.","DOI":"10.1109\/CVPR.2018.00441"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"672","DOI":"10.1038\/s41586-021-03854-z","article-title":"Skilful precipitation nowcasting using deep generative models of radar","volume":"597","author":"Ravuri","year":"2021","journal-title":"Nature"},{"key":"ref_7","unstructured":"Han, J., Lombardo, S., Schroers, C., and Mandt, S. (2019, January 8\u201314). Deep generative video compression. Proceedings of the International Conference on Neural Information Processing Systems, Vancouver, BC, Canada."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Lu, G., Ouyang, W., Xu, D., Zhang, X., Cai, C., and Gao, Z. (2019, January 16\u201320). Dvc: An end-to-end deep video compression framework. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Long Beach, CA, USA.","DOI":"10.1109\/CVPR.2019.01126"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Agustsson, E., Minnen, D., Johnston, N., Balle, J., Hwang, S.J., and Toderici, G. (2020, January 14\u201319). Scale-space flow for end-to-end optimized video compression. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Virtually.","DOI":"10.1109\/CVPR42600.2020.00853"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1109\/JSTSP.2020.3043590","article-title":"Learning for video compression with recurrent auto-encoder and recurrent probability model","volume":"15","author":"Yang","year":"2020","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_11","unstructured":"Yang, R., Yang, Y., Marino, J., and Mandt, S. (2021, January 3\u20137). Hierarchical Autoregressive Modeling for Neural Video Compression. Proceedings of the International Conference on Learning Representations, Virtually."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Yang, Y., Mandt, S., and Theis, L. (2022). An Introduction to Neural Data Compression. arXiv.","DOI":"10.1561\/9781638281757"},{"key":"ref_13","unstructured":"Babaeizadeh, M., Finn, C., Erhan, D., Campbell, R.H., and Levine, S. (May, January 30). Stochastic Variational Video Prediction. Proceedings of the International Conference on Learning Representations, Vancouver, BC, Canada."},{"key":"ref_14","unstructured":"Denton, E., and Fergus, R. (2018, January 10\u201315). Stochastic video generation with a learned prior. Proceedings of the International Conference on Machine Learning, Alvsjo, Sweden."},{"key":"ref_15","unstructured":"Castrejon, L., Ballas, N., and Courville, A. (November, January 27). Improved conditional vrnns for video prediction. Proceedings of the IEEE\/CVF International Conference on Computer Vision, Seoul, Republic of Korea."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Aigner, S., and K\u00f6rner, M. (2018). Futuregan: Anticipating the future frames of video sequences using spatio-temporal 3d convolutions in progressively growing gans. arXiv.","DOI":"10.5194\/isprs-archives-XLII-2-W16-3-2019"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Kwon, Y.H., and Park, M.G. (2019, January 16\u201320). Predicting future frames using retrospective cycle gan. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Long Beach, CA, USA.","DOI":"10.1109\/CVPR.2019.00191"},{"key":"ref_18","unstructured":"Lee, A.X., Zhang, R., Ebert, F., Abbeel, P., Finn, C., and Levine, S. (2018). Stochastic adversarial video prediction. arXiv."},{"key":"ref_19","unstructured":"Sohl-Dickstein, J., Weiss, E., Maheswaranathan, N., and Ganguli, S. (2015, January 6\u201311). Deep unsupervised learning using nonequilibrium thermodynamics. Proceedings of the International Conference on Machine Learning, Lille, France."},{"key":"ref_20","unstructured":"Song, Y., and Ermon, S. (2019, January 8\u201314). Generative modeling by estimating gradients of the data distribution. Proceedings of the Advances in Neural Information Processing Systems 32 (NeurIPS 2019), Vancouver, BC, Canada."},{"key":"ref_21","first-page":"6840","article-title":"Denoising diffusion probabilistic models","volume":"33","author":"Ho","year":"2020","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_22","unstructured":"Song, Y., Sohl-Dickstein, J., Kingma, D.P., Kumar, A., Ermon, S., and Poole, B. (2021, January 3\u20137). Score-Based Generative Modeling through Stochastic Differential Equations. Proceedings of the International Conference on Learning Representations, Virtually."},{"key":"ref_23","first-page":"1415","article-title":"Maximum likelihood training of score-based diffusion models","volume":"34","author":"Song","year":"2021","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1038\/4580","article-title":"Predictive coding in the visual cortex: A functional interpretation of some extra-classical receptive-field effects","volume":"2","author":"Rao","year":"1999","journal-title":"Nat. Neurosci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1162\/neco_a_01458","article-title":"Predictive coding, variational autoencoders, and biological connections","volume":"34","author":"Marino","year":"2021","journal-title":"Neural Comput."},{"key":"ref_26","unstructured":"Yang, R., Yang, Y., Marino, J., and Mandt, S. (2021). Insights from Generative Modeling for Neural Video Compression. arXiv."},{"key":"ref_27","unstructured":"Marino, J., Chen, L., He, J., and Mandt, S. (2021, January 22). Improving sequential latent variable models with autoregressive flows. Proceedings of the 2nd Symposium on Advances in Approximate Bayesian Inference, Virtually."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Akan, A.K., Erdem, E., Erdem, A., and Guney, F. (2021, January 11\u201317). Slamp: Stochastic Latent Appearance and Motion Prediction. Proceedings of the IEEE\/CVF International Conference on Computer Vision (ICCV), Virtually.","DOI":"10.1109\/ICCV48922.2021.01446"},{"key":"ref_29","unstructured":"Clark, A., Donahue, J., and Simonyan, K. (2019). Adversarial video generation on complex datasets. arXiv."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Dorkenwald, M., Milbich, T., Blattmann, A., Rombach, R., Derpanis, K.G., and Ommer, B. (2021, January 19\u201325). Stochastic image-to-video synthesis using cinns. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Virtually.","DOI":"10.1109\/CVPR46437.2021.00374"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Nam, S., Ma, C., Chai, M., Brendel, W., Xu, N., and Kim, S.J. (2019, January 16\u201320). End-to-end time-lapse video synthesis from a single outdoor image. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Long Beach, CA, USA.","DOI":"10.1109\/CVPR.2019.00150"},{"key":"ref_32","unstructured":"Wu, C., Huang, L., Zhang, Q., Li, B., Ji, L., Yang, F., Sapiro, G., and Duan, N. (2021). Godiva: Generating open-domain videos from natural descriptions. arXiv."},{"key":"ref_33","unstructured":"Singer, U., Polyak, A., Hayes, T., Yin, X., An, J., Zhang, S., Hu, Q., Yang, H., Ashual, O., and Gafni, O. (2022). Make-a-video: Text-to-video generation without text-video data. arXiv."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Gafni, O., Polyak, A., Ashual, O., Sheynin, S., Parikh, D., and Taigman, Y. (2022, January 23\u201327). Make-a-scene: Scene-based text-to-image generation with human priors. Proceedings of the Computer Vision\u2013ECCV 2022: 17th European Conference, Tel Aviv, Israel.","DOI":"10.1007\/978-3-031-19784-0_6"},{"key":"ref_35","unstructured":"Ramesh, A., Dhariwal, P., Nichol, A., Chu, C., and Chen, M. (2022). Hierarchical text-conditional image generation with clip latents. arXiv."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Zhang, H., Koh, J.Y., Baldridge, J., Lee, H., and Yang, Y. (2021, January 19\u201325). Cross-modal contrastive learning for text-to-image generation. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Virtually.","DOI":"10.1109\/CVPR46437.2021.00089"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Zhou, Y., Zhang, R., Chen, C., Li, C., Tensmeyer, C., Yu, T., Gu, J., Xu, J., and Sun, T. (2022, January 19\u201324). LAFITE: Towards Language-Free Training for Text-to-Image Generation. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR), New Orleans, LA, USA.","DOI":"10.1109\/CVPR52688.2022.01738"},{"key":"ref_38","unstructured":"Wang, T.C., Liu, M.Y., Zhu, J.Y., Liu, G., Tao, A., Kautz, J., and Catanzaro, B. (2018). Video-to-Video Synthesis. arXiv."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2586","DOI":"10.1007\/s11263-020-01333-y","article-title":"Train sparsely, generate densely: Memory-efficient unsupervised training of high-resolution temporal gan","volume":"128","author":"Saito","year":"2020","journal-title":"Int. J. Comput. Vis."},{"key":"ref_40","unstructured":"Yu, S., Tack, J., Mo, S., Kim, H., Kim, J., Ha, J.W., and Shin, J. (2022, January 25\u201329). Generating Videos with Dynamics-aware Implicit Generative Adversarial Networks. Proceedings of the International Conference on Learning Representations, Virtually."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Byeon, W., Wang, Q., Srivastava, R.K., and Koumoutsakos, P. (2018, January 8\u201314). Contextvp: Fully context-aware video prediction. Proceedings of the European Conference on Computer Vision (ECCV), Munich, Germany.","DOI":"10.1007\/978-3-030-01270-0_46"},{"key":"ref_42","unstructured":"Finn, C., Goodfellow, I., and Levine, S. (2016, January 5\u201310). Unsupervised learning for physical interaction through video prediction. Proceedings of the 30th Conference on Neural Information Processing Systems (NIPS 2016), Barcelona, Spain."},{"key":"ref_43","unstructured":"Lotter, W., Kreiman, G., and Cox, D. (2017, January 24\u201326). Deep Predictive Coding Networks for Video Prediction and Unsupervised Learning. Proceedings of the International Conference on Learning Representations, Palais des Congres Neptune, France."},{"key":"ref_44","unstructured":"Srivastava, N., Mansimov, E., and Salakhutdinov, R. (2015, January 6\u201311). Unsupervised Learning of Video Representations using LSTMs. Proceedings of the International Conference on Machine Learning, Lille, France."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Walker, J., Gupta, A., and Hebert, M. (2015, January 11\u201318). Dense optical flow prediction from a static image. Proceedings of the IEEE International Conference on Computer Vision, Santiago, Chile.","DOI":"10.1109\/ICCV.2015.281"},{"key":"ref_46","unstructured":"Villegas, R., Yang, J., Hong, S., Lin, X., and Lee, H. (2017, January 24\u201326). Decomposing Motion and Content for Natural Video Sequence Prediction. Proceedings of the International Conference on Learning Representations, Palais des Congres Neptune, France."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Liang, X., Lee, L., Dai, W., and Xing, E.P. (2017, January 22\u201329). Dual motion GAN for future-flow embedded video prediction. Proceedings of the IEEE International Conference on Computer Vision, Venice, Italy.","DOI":"10.1109\/ICCV.2017.194"},{"key":"ref_48","unstructured":"Li, Y., and Mandt, S. (2018, January 10\u201315). Disentangled sequential autoencoder. Proceedings of the International Conference on Machine Learning, Alvsjo, Sweden."},{"key":"ref_49","unstructured":"Kumar, M., Babaeizadeh, M., Erhan, D., Finn, C., Levine, S., Dinh, L., and Kingma, D. (2019). Videoflow: A flow-based generative model for video. arXiv."},{"key":"ref_50","unstructured":"Unterthiner, T., van Steenkiste, S., Kurach, K., Marinier, R., Michalski, M., and Gelly, S. (2018). Towards accurate generative models of video: A new metric & challenges. arXiv."},{"key":"ref_51","unstructured":"Villegas, R., Pathak, A., Kannan, H., Erhan, D., Le, Q.V., and Lee, H. (2019, January 8\u201314). High fidelity video prediction with large stochastic recurrent neural networks. Proceedings of the Advances in Neural Information Processing Systems, Vancouver, BC, Canada."},{"key":"ref_52","unstructured":"Babaeizadeh, M., Saffar, M.T., Nair, S., Levine, S., Finn, C., and Erhan, D. (2021). Fitvid: Overfitting in pixel-level video prediction. arXiv."},{"key":"ref_53","unstructured":"Villegas, R., Erhan, D., and Lee, H. (2018, January 10\u201315). Hierarchical long-term video prediction without supervision. Proceedings of the International Conference on Machine Learning, Alvsjo, Sweden."},{"key":"ref_54","unstructured":"Yan, W., Zhang, Y., Abbeel, P., and Srinivas, A. (2021). Videogpt: Video generation using vq-vae and transformers. arXiv."},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Rakhimov, R., Volkhonskiy, D., Artemov, A., Zorin, D., and Burnaev, E. (2020). Latent video transformer. arXiv.","DOI":"10.5220\/0010241801010112"},{"key":"ref_56","unstructured":"Lee, W., Jung, W., Zhang, H., Chen, T., Koh, J.Y., Huang, T., Yoon, H., Lee, H., and Hong, S. (2021, January 3\u20137). Revisiting Hierarchical Approach for Persistent Long-Term Video Prediction. Proceedings of the International Conference on Learning Representations, Virtually."},{"key":"ref_57","unstructured":"Bayer, J., and Osendorfer, C. (2014). Learning stochastic recurrent networks. arXiv."},{"key":"ref_58","unstructured":"Chung, J., Kastner, K., Dinh, L., Goel, K., Courville, A.C., and Bengio, Y. (2015). A recurrent latent variable model for sequential data. arXiv."},{"key":"ref_59","doi-asserted-by":"crossref","unstructured":"Wu, B., Nair, S., Martin-Martin, R., Fei-Fei, L., and Finn, C. (2021, January 19\u201325). Greedy hierarchical variational autoencoders for large-scale video prediction. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Virtually.","DOI":"10.1109\/CVPR46437.2021.00235"},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Zhao, L., Peng, X., Tian, Y., Kapadia, M., and Metaxas, D. (2018, January 8\u201314). Learning to forecast and refine residual motion for image-to-video generation. Proceedings of the European Conference on Computer Vision (ECCV), Munich, Germany.","DOI":"10.1007\/978-3-030-01267-0_24"},{"key":"ref_61","unstructured":"Franceschi, J.Y., Delasalles, E., Chen, M., Lamprier, S., and Gallinari, P. (2020, January 13\u201318). Stochastic Latent Residual Video Prediction. Proceedings of the 37th International Conference on Machine Learning, Virtually."},{"key":"ref_62","doi-asserted-by":"crossref","unstructured":"Blau, Y., and Michaeli, T. (2018, January 18\u201322). The perception-distortion tradeoff. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Salt Lake City, UT, USA.","DOI":"10.1109\/CVPR.2018.00652"},{"key":"ref_63","unstructured":"Vondrick, C., Pirsiavash, H., and Torralba, A. (2016, January 5\u201310). Generating videos with scene dynamics. Proceedings of the 30th Conference on Neural Information Processing Systems (NIPS 2016), Barcelona, Spain."},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"Tulyakov, S., Liu, M.Y., Yang, X., and Kautz, J. (2018, January 18\u201322). Mocogan: Decomposing motion and content for video generation. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Salt Lake City, UT, USA.","DOI":"10.1109\/CVPR.2018.00165"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"3313","DOI":"10.1109\/TKDE.2021.3130191","article-title":"A Review on Generative Adversarial Networks: Algorithms, Theory, and Applications","volume":"35","author":"Gui","year":"2021","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_66","doi-asserted-by":"crossref","unstructured":"Saharia, C., Ho, J., Chan, W., Salimans, T., Fleet, D.J., and Norouzi, M. (2021). Image super-resolution via iterative refinement. arXiv.","DOI":"10.1109\/TPAMI.2022.3204461"},{"key":"ref_67","unstructured":"Pandey, K., Mukherjee, A., Rai, P., and Kumar, A. (2022). DiffuseVAE: Efficient, Controllable and High-Fidelity Generation from Low-Dimensional Latents. arXiv."},{"key":"ref_68","unstructured":"Chen, N., Zhang, Y., Zen, H., Weiss, R.J., Norouzi, M., and Chan, W. (2021, January 3\u20137). WaveGrad: Estimating Gradients for Waveform Generation. Proceedings of the International Conference on Learning Representations, Virtually."},{"key":"ref_69","unstructured":"Kong, Z., Ping, W., Huang, J., Zhao, K., and Catanzaro, B. (2021, January 3\u20137). DiffWave: A Versatile Diffusion Model for Audio Synthesis. Proceedings of the International Conference on Learning Representations, Virtually."},{"key":"ref_70","doi-asserted-by":"crossref","unstructured":"Luo, S., and Hu, W. (2021, January 19\u201325). Diffusion probabilistic models for 3d point cloud generation. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Virtually.","DOI":"10.1109\/CVPR46437.2021.00286"},{"key":"ref_71","unstructured":"Rasul, K., Seward, C., Schuster, I., and Vollgraf, R. (2021, January 18\u201324). Autoregressive denoising diffusion models for multivariate probabilistic time series forecasting. Proceedings of the International Conference on Machine Learning, Virtually."},{"key":"ref_72","unstructured":"Ho, J., Salimans, T., Gritsenko, A., Chan, W., Norouzi, M., and Fleet, D.J. (2022). Video Diffusion Models. arXiv."},{"key":"ref_73","unstructured":"Voleti, V., Jolicoeur-Martineau, A., and Pal, C. (December, January 28). MCVD-Masked Conditional Video Diffusion for Prediction, Generation, and Interpolation. Proceedings of the Advances in Neural Information Processing Systems, New Orleans, LA, USA."},{"key":"ref_74","unstructured":"Brock, A., Donahue, J., and Simonyan, K. (2019, January 6\u20139). Large Scale GAN Training for High Fidelity Natural Image Synthesis. Proceedings of the International Conference on Learning Representations, New Orleans, LA, USA."},{"key":"ref_75","unstructured":"Kingma, D.P., and Welling, M. (2013). Auto-encoding variational bayes. arXiv."},{"key":"ref_76","unstructured":"Papamakarios, G., Pavlakou, T., and Murray, I. (2017, January 4\u20139). Masked autoregressive flow for density estimation. Proceedings of the Advances in Neural Information Processing Systems 30 (NIPS 2017), Long Beach, CA, USA."},{"key":"ref_77","unstructured":"Schapire, R.E. (August, January 31). A brief introduction to boosting. Proceedings of the Ijcai, Stockholm, Sweden."},{"key":"ref_78","unstructured":"Nichol, A.Q., and Dhariwal, P. (2021, January 18\u201324). Improved denoising diffusion probabilistic models. Proceedings of the International Conference on Machine Learning, Virtually."},{"key":"ref_79","unstructured":"Kolen, J.F., and Kremer, S.C. (2001). A Field Guide to Dynamical Recurrent Networks, John Wiley & Sons."},{"key":"ref_80","unstructured":"Ebert, F., Finn, C., Lee, A.X., and Levine, S. (2017, January 13\u201315). Self-Supervised Visual Planning with Temporal Skip Connections. Proceedings of the CoRL, Mountain View, CA, USA."},{"key":"ref_81","doi-asserted-by":"crossref","unstructured":"Schuldt, C., Laptev, I., and Caputo, B. (2004, January 23\u201326). Recognizing human actions: A local SVM approach. Proceedings of the 17th International Conference on Pattern Recognition, Cambridge, UK.","DOI":"10.1109\/ICPR.2004.1334462"},{"key":"ref_82","unstructured":"Cordts, M., Omran, M., Ramos, S., Rehfeld, T., Enzweiler, M., Benenson, R., Franke, U., Roth, S., and Schiele, B. (July, January 26). The Cityscapes Dataset for Semantic Urban Scene Understanding. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Las Vegas, NV, USA."},{"key":"ref_83","unstructured":"Chirila, D.B. (2018). Towards Lattice Boltzmann Models for Climate Sciences: The GeLB Programming Language with Applications. [Ph.D. Thesis, Universit\u00e4t Bremen]."},{"key":"ref_84","unstructured":"Unterthiner, T., van Steenkiste, S., Kurach, K., Marinier, R., Michalski, M., and Gelly, S. (2019, January 6\u20139). FVD: A new metric for video generation. Proceedings of the ICLR 2019 Workshop for Deep Generative Models for Highly Structured Data, New Orleans, LA, USA."},{"key":"ref_85","doi-asserted-by":"crossref","unstructured":"Zhang, R., Isola, P., Efros, A.A., Shechtman, E., and Wang, O. (2018, January 18\u201322). The unreasonable effectiveness of deep features as a perceptual metric. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Salt Lake City, UT, USA.","DOI":"10.1109\/CVPR.2018.00068"},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"1087","DOI":"10.1287\/mnsc.22.10.1087","article-title":"Scoring rules for continuous probability distributions","volume":"22","author":"Matheson","year":"1976","journal-title":"Manag. Sci."},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1175\/1520-0434(2000)015<0559:DOTCRP>2.0.CO;2","article-title":"Decomposition of the continuous ranked probability score for ensemble prediction systems","volume":"15","author":"Hersbach","year":"2000","journal-title":"Weather Forecast."},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1198\/jbes.2010.08110","article-title":"Comparing density forecasts using threshold-and quantile-weighted scoring rules","volume":"29","author":"Gneiting","year":"2011","journal-title":"J. Bus. Econ. Stat."},{"key":"ref_89","unstructured":"Smaira, L., Carreira, J., Noland, E., Clancy, E., Wu, A., and Zisserman, A. (2020). A short note on the kinetics-700-2020 human action dataset. arXiv."},{"key":"ref_90","unstructured":"Song, J., Meng, C., and Ermon, S. (2021, January 3\u20137). Denoising Diffusion Implicit Models. Proceedings of the International Conference on Learning Representations, Virtually."},{"key":"ref_91","unstructured":"Salimans, T., and Ho, J. (2022). Progressive distillation for fast sampling of diffusion models. arXiv."},{"key":"ref_92","doi-asserted-by":"crossref","unstructured":"Ronneberger, O., Fischer, P., and Brox, T. (2015, January 5\u20139). U-net: Convolutional networks for biomedical image segmentation. Proceedings of the International Conference on Medical Image Computing and Computer-Assisted Intervention, Munich, Germany.","DOI":"10.1007\/978-3-319-24574-4_28"},{"key":"ref_93","unstructured":"He, K., Zhang, X., Ren, S., and Sun, J. (July, January 26). Deep residual learning for image recognition. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Las Vegas, NV, USA."},{"key":"ref_94","unstructured":"Ballas, N., Yao, L., Pal, C., and Courville, A.C. (2016, January 2\u20134). Delving Deeper into Convolutional Networks for Learning Video Representations. Proceedings of the ICLR (Poster), San Juan, Puerto Rico."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/10\/1469\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:09:13Z","timestamp":1760130553000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/10\/1469"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,20]]},"references-count":94,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2023,10]]}},"alternative-id":["e25101469"],"URL":"https:\/\/doi.org\/10.3390\/e25101469","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,10,20]]}}}