{"product_id":"110183","title":"Mathematics of the diffusion model ","description":"\u003ccenter\u003e\u003cdiv style=\"text-align:center\"\u003e\u003cimg src=\"https:\/\/tmgdisk01.cafe24.com\/images\/vs\/4172\/sv\/3jYEEJoChBmAPJQnGYrfku60TxiVUj.png?v=1765096117\" style=\"max-width:100%;max-height:10px\"\u003e\u003c\/div\u003e\u003c\/center\u003e\n\u003ccenter\u003e\u003ctable\u003e\u003ctr\u003e\u003ctd style=\"height:10px\"\u003e\u003c\/td\u003e\u003c\/tr\u003e\u003c\/table\u003e\u003c\/center\u003e\n\u003ccenter\u003e\u003ctable\u003e\u003ctr\u003e\u003ctd style=\"height:10px\"\u003e\u003c\/td\u003e\u003c\/tr\u003e\u003c\/table\u003e\u003c\/center\u003e\n\u003ccenter\u003e\n\n\u003cdiv style=\"width:95%\"\u003e\n\n\u003cdiv style=\"text-align:center;font-size:30px;font-weight:bolder;line-height:1.6em\"\u003e Mathematics of the diffusion model \u003c\/div\u003e\n\n\u003ccenter\u003e\u003ctable\u003e\u003ctr\u003e\u003ctd style=\"height:10px\"\u003e\u003c\/td\u003e\u003c\/tr\u003e\u003c\/table\u003e\u003c\/center\u003e\n\n\u003ccenter\u003e\u003ctable\u003e\u003ctr\u003e\u003ctd style=\"height:10px\"\u003e\u003c\/td\u003e\u003c\/tr\u003e\u003c\/table\u003e\u003c\/center\u003e\n\n\u003ccenter\u003e\u003ctable\u003e\u003ctr\u003e\u003ctd style=\"height:10px\"\u003e\u003c\/td\u003e\u003c\/tr\u003e\u003c\/table\u003e\u003c\/center\u003e\n\n\u003ccenter\u003e\u003ctable\u003e\u003ctr\u003e\u003ctd style=\"height:10px\"\u003e\u003c\/td\u003e\u003c\/tr\u003e\u003c\/table\u003e\u003c\/center\u003e\n\n\u003cdiv style=\"border-bottom:1px;border-bottom-style:dotted;border-color:;padding-bottom:20px\"\u003e\u003ccenter\u003e\u003ctable align=\"center\" width=\"100%\"\u003e\u003ctbody style=\"border:0px\"\u003e\n\n\u003ctr\u003e\u003ctd align=\"center\" style=\"line-height:1.2em;text-align:center;font-size:18px;color:black;font-weight:bold;padding-bottom:20px;\"\u003e\u003c\/td\u003e\u003c\/tr\u003e\n\n\u003ctr\u003e\u003ctd style=\"text-align:center\"\u003e\u003cimg src=\"https:\/\/image.yes24.com\/goods\/128125394\/XL\" style=\"max-width:100%;height:auto\"\u003e\u003c\/td\u003e\u003c\/tr\u003e\n\n\n\u003c\/tbody\u003e\u003c\/table\u003e\u003c\/center\u003e\u003c\/div\u003e\n\n\u003ccenter\u003e\u003ctable\u003e\u003ctr\u003e\u003ctd style=\"height:10px\"\u003e\u003c\/td\u003e\u003c\/tr\u003e\u003c\/table\u003e\u003c\/center\u003e\n\n\u003ccenter\u003e\u003ctable\u003e\u003ctr\u003e\u003ctd style=\"height:10px\"\u003e\u003c\/td\u003e\u003c\/tr\u003e\u003c\/table\u003e\u003c\/center\u003e\n\n\u003cdiv style=\"width:95%;{split_style6}padding-top:20px;padding-bottom:20px\"\u003e\n\n\u003cdiv style=\"text-align:left;font-size:16px;font-weight:bold;padding-bottom:20px\"\u003e Description \u003c\/div\u003e\n\n\u003cdiv style=\"text-align:left;word-break:break-all;font-size:14px;line-height:1.6em;\"\u003e\n\n\u003cdiv\u003e\u003ch5\u003e \u003cb\u003eBook Introduction\u003c\/b\u003e\n\u003c\/h5\u003e\u003c\/div\u003e\n\u003cdiv\u003e\n\u003cdiv\u003e\u003cdiv\u003e \u003cb\u003eMathematical principles of diffusion model technology for generating images\/videos\/voices\/texts\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e The diffusion model is attracting attention as a generative model that creates high-quality data based on technologies such as DALL-E2, Midjourney, and Stable Diffusion that generate images corresponding to text.\u003cbr\u003e This book explains in great detail the basic concepts of the diffusion model, its development process, and application examples.\u003cbr\u003e By examining the principles of the diffusion model mathematically, we can better understand the theory and draw out the high potential of the diffusion model.\u003cbr\u003e\u003cbr\u003e\n\u003c\/div\u003e\u003c\/div\u003e\n\u003cdiv\u003e\u003cul\u003e\u003cli\u003e You can preview some of the book's contents.\u003cbr\u003e \u003cspan\u003ePreview\u003c\/span\u003e\n\n\u003c\/li\u003e\u003c\/ul\u003e\u003c\/div\u003e\n\u003c\/div\u003e\n\u003cbr\u003e\u003cdiv\u003e\u003ch5\u003e \u003cb\u003eindex\u003c\/b\u003e\n\u003c\/h5\u003e\u003c\/div\u003e\n\u003cdiv\u003e\n\u003cdiv\u003e Translator's Preface viii\u003cbr\u003e Recommendation ix\u003cbr\u003e Preface xi \u003cbr\u003eList of symbols xv\u003cbr\u003e\u003cbr\u003e \u003cb\u003eCHAPTER 1 Generative Model 1\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e 1.1 What is a generative model? 1\u003cbr\u003e 1.2 Energy-based model and distribution function 4\u003cbr\u003e 1.3 Learning Method 6\u003cbr\u003e 1.4 The Difficulty of Generating Multimodal Data in High Dimensions 13\u003cbr\u003e 1.5 Score: Slope 14 for log-likelihood input\u003cbr\u003e __1.5.1 Langevin Monte Carlo Method 16\u003cbr\u003e __1.5.2 Score Matching 18\u003cbr\u003e __1.5.3 Implicit Score Matching 19\u003cbr\u003e __1.5.4 Proof that implicit score matching can estimate scores 22\u003cbr\u003e __1.5.5 Denoising Score Matching 26\u003cbr\u003e __1.5.6 Proof that denoising score matching can estimate scores 30\u003cbr\u003e __1.5.7 Proof when noise follows a normal distribution 32\u003cbr\u003e __1.5.8 Summary of Score Matching Methods 37\u003cbr\u003e Summary 37\u003cbr\u003e\u003cbr\u003e \u003cb\u003eCHAPTER 2 Diffusion Models 39\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e 2.1 Score-based models and denoising diffusion probability models 39\u003cbr\u003e 2.2 Score-based model 40\u003cbr\u003e __2.2.1 Problems with the Langevin Monte Carlo Method Using Estimated Scores 40\u003cbr\u003e __2.2.2 Score-based models combine scores from multiple post-perturbation distributions 42\u003cbr\u003e 2.3 Denoising Diffusion Probability Model 46 \u003cbr\u003e__2.3.1 Latent variable model consisting of diffusion and reverse diffusion processes 46\u003cbr\u003e __2.3.2 DDPM Learning 51\u003cbr\u003e __2.3.3 56 with denoising score matching in DDPM\u003cbr\u003e __2.3.4 Data Generation Using DDPM 61\u003cbr\u003e 2.4 Unified structure using signal-to-noise ratio of SBM and DDPM 62\u003cbr\u003e __2.4.1 Relationship between SBM and DDPM 62\u003cbr\u003e __2.4.2 Continuous Time Model 70\u003cbr\u003e __2.4.3 The same solution can be obtained regardless of the noise schedule 71\u003cbr\u003e __2.4.4 Learnable Noise Schedule 72\u003cbr\u003e Summary 73\u003cbr\u003e\u003cbr\u003e \u003cb\u003eCHAPTER 3 Continuous Time Diffusion Models 75\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e 3.1 Stochastic Differential Equations 76\u003cbr\u003e 3.2 SDE Representation of SBM and DDPM 77\u003cbr\u003e 3.3 De-diffusion process of SDE expression 80\u003cbr\u003e 3.4 Learning the SDE Representation Diffusion Model 81\u003cbr\u003e 3.5 SDE Expression Diffusion Model Sampling 83\u003cbr\u003e 3.6 Probability Flow ODE 84\u003cbr\u003e __3.6.1 Proof that the marginal likelihoods of the probability flow ODE and SDE are identical 86\u003cbr\u003e __3.6.2 Likelihood Calculation for Probabilistic Flow ODEs 88\u003cbr\u003e __3.6.3 Probability Flow in Signal and Noise ODE 88\u003cbr\u003e 3.7 Characteristics of the Diffusion Model 89\u003cbr\u003e __3.7.1 Relationship with Existing Latent Variable Models 90 \u003cbr\u003e__3.7.2 The diffusion model is stable in learning 91\u003cbr\u003e __3.7.3 Decomposing complex generation problems into simpler sub-generation problems 92\u003cbr\u003e __3.7.4 Various conditions can be combined 93\u003cbr\u003e __3.7.5 The symmetry of creation can be introduced naturally 94\u003cbr\u003e __3.7.6 When extracting samples, the number of steps is large, so the generation speed is slow 95\u003cbr\u003e __3.7.7 Unresolved issue of how to generalize to the diffusion model 95\u003cbr\u003e Summary 96\u003cbr\u003e\u003cbr\u003e \u003cb\u003eCHAPTER 4 EVOLUTION OF THE DIFFUSION MODEL 97\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e 4.1 Score 97 in conditional generation\u003cbr\u003e 4.2 Classifier Guidance 98\u003cbr\u003e 4.3 Guidance 99 without using a classifier\u003cbr\u003e 4.4 Subspace Diffusion Model 102\u003cbr\u003e __4.4.1 Learning the Subspace Diffusion Model 104\u003cbr\u003e __4.4.2 Sampling of Subspace Diffusion Models 106\u003cbr\u003e 4.5 Diffusion Model Considering Symmetry 107\u003cbr\u003e __4.5.1 Geometry and Symmetry 107\u003cbr\u003e __4.5.2 Rotational arrangement of compounds 110\u003cbr\u003e Summary 117\u003cbr\u003e\u003cbr\u003e \u003cb\u003eCHAPTER 5 APPLICATIONS 119\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e 5.1 Image Generation, Super-Resolution, Complementation, and Image Transformation 120\u003cbr\u003e 5.2 Creating Videos and Panoramas 121\u003cbr\u003e 5.3 Semantic Extraction and Transformation 122 \u003cbr\u003e5.4 Voice Synthesis and Emphasis 123\u003cbr\u003e 5.5 Formation and Rotation of Compounds 124\u003cbr\u003e 5.6 Improving Robustness to Adversarial Perturbations 125\u003cbr\u003e 5.7 Data Compression 126\u003cbr\u003e Summary 127\u003cbr\u003e\u003cbr\u003e \u003cb\u003eAPPENDIX A Appendix 129\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e A.1 Posterior probability distribution when the prior distribution is normal and the likelihood is linearly normal 129\u003cbr\u003e A.2 ELBO 130\u003cbr\u003e A.3 Deriving a Probabilistic Flow ODE Using Signal and Noise 131\u003cbr\u003e A.4 Conditional Generation Problem 135\u003cbr\u003e A.5 Denoising Implicit Diffusion Model 137\u003cbr\u003e A.6 Proof of the Stochastic Differential Equation for the Inverse Diffusion Process 141\u003cbr\u003e A.7 Diffusion Model with Non-Gaussian Noise 146\u003cbr\u003e A.8 Analog Bits: Discrete Variable Diffusion Model 147\u003cbr\u003e\u003cbr\u003e Reference 149\u003cbr\u003e Search 154\u003c\/div\u003e\n\u003cdiv\u003e\u003c\/div\u003e\n\u003c\/div\u003e\n\u003cbr\u003e\u003cdiv\u003e\u003ch5\u003e \u003cb\u003eDetailed image\u003c\/b\u003e \u003c\/h5\u003e\u003c\/div\u003e\n\u003cdiv\u003e\u003cdiv\u003e\u003cimg src=\"https:\/\/image.yes24.com\/momo\/TopCate4565\/MidCate003\/456424428.jpg\" border=\"0\" alt=\"Detailed Image 1\"\u003e\u003c\/div\u003e\u003c\/div\u003e\n\u003cbr\u003e\u003cdiv\u003e\u003ch5\u003e \u003cb\u003eInto the book\u003c\/b\u003e\n\u003c\/h5\u003e\u003c\/div\u003e\n\u003cdiv\u003e\n\u003cdiv\u003e\n\u003cdiv\u003e A generative model is a model that generates data in the target domain.\u003cbr\u003e And some generative models can also evaluate the likelihood p(x) of given data x. \u003cbr\u003eUnderstanding how data is generated is one effective way to understand it, and being able to generate data freely can be beneficial to many applications.\u003cbr\u003e So, a lot of research has been done on generative models for a long time.\u003cbr\u003e\u003cbr\u003e --- p.1\u003cbr\u003e\u003cbr\u003e The first is the score-based model (SBM).\u003cbr\u003e As we saw in Chapter 1, we can obtain samples from the target probability distribution using the Langevin Monte Carlo method, which uses scores estimated by denoising score matching.\u003cbr\u003e However, in practice, there are problems with score estimation, sampling takes a very long time, and sampling does not work well in high-dimensional multimodal distributions.\u003cbr\u003e To address this issue, we examine learning scores from distributions perturbed by noise of different sizes and generating data using the Langevin Monte Carlo method.\u003cbr\u003e\u003cbr\u003e --- p.39\u003cbr\u003e \u003cbr\u003eProbabilistic flow ODEs can be viewed as a special form of neural ODEs, which are generative models using ODEs.\u003cbr\u003e Neural ODE models the change in each time step using a neural network by changing the data extracted from the prior distribution using differential equations.\u003cbr\u003e The probability flow ODE defines this change amount based on the previous equation (3.6).\u003cbr\u003e\u003cbr\u003e --- p.85\u003cbr\u003e\u003cbr\u003e Guidance that does not use a classifier can solve the classifier guidance problem.\u003cbr\u003e There is no need to train the classifier separately from the unconditional scores at various noise levels, and in general training, the conditions can be dropped out with a certain probability.\u003cbr\u003e So, learning can be greatly simplified.\u003cbr\u003e Additionally, by sharing the learning of conditional and unconditional scores, we can significantly improve the generation quality by reducing the possibility of discovering relationships between y and x that are actually unrelated.\u003cbr\u003e\u003cbr\u003e --- p.101\u003cbr\u003e \u003cbr\u003eVideo generation, which was the most difficult task to learn, is also being implemented using a diffusion model.\u003cbr\u003e Video generation can be viewed as the problem of generating an image for each frame.\u003cbr\u003e Video generation deals with a very high-dimensional data generation problem, so it was difficult to even overfit the training data.\u003cbr\u003e Video generation using a diffusion model is a method of generating some frames and using them as conditions.\u003cbr\u003e\n\n\u003c\/div\u003e\n\u003cdiv\u003e --- p.121\u003c\/div\u003e\n\u003c\/div\u003e\n\u003cdiv\u003e\u003c\/div\u003e\n\u003c\/div\u003e\n\u003cbr\u003e\u003cdiv\u003e\u003ch5\u003e \u003cb\u003ePublisher's Review\u003c\/b\u003e\n\u003c\/h5\u003e\u003c\/div\u003e\n\u003cdiv\u003e\n\u003cdiv\u003e \u003cb\u003eUnderstanding Diffusion Models with Formulas and Figures\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e We've all witnessed the impact of advances in AI that generate images from text, such as DALL-E2, Midjourney, and Stable Diffusion.\u003cbr\u003e The basis of these technologies is the diffusion model.\u003cbr\u003e Understanding the proliferation models that generate high-quality data is essential to understanding today's generative AI, but relevant literature is scarce.\u003cbr\u003e  \u003cbr\u003eThis book explains in detail the basic concepts of the diffusion model, its development process, and application cases.\u003cbr\u003e To help you understand the formula more intuitively, we provide several figures and graphs, and by comparing learning stability, likelihood estimation, and conditional generation with existing generative models, you can clearly understand the diffusion model.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e What makes this book even more special is that it was written by Daisuke Okanohara, Chief Research Officer of Preferred Networks, Japan's leading AI company.\u003cbr\u003e Daisuke Okanohara, a veteran author who is praised for “providing a rich context surrounding technology,” won the 32nd Okawa Publishing Award for this book.\u003cbr\u003e If you want to properly understand the diffusion model at the heart of artificial intelligence today, this book will serve as a guide.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e \u003cb\u003eKey Contents\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003e ● Overview and basic concepts of the generative model\u003cbr\u003e ● Understanding diffusion models using SNR and score-based models \u003cbr\u003e● Features of continuous-time diffusion models and diffusion models\u003cbr\u003e ● Development of diffusion models such as classifier guidance, subspace, and symmetry\u003cbr\u003e ● Application examples of diffusion models such as video, voice synthesis, and compounds \u003c\/div\u003e\n\u003cdiv\u003e\u003c\/div\u003e\n\u003c\/div\u003e\n\u003c\/div\u003e\n\n\n\u003c\/div\u003e\n\n\u003ccenter\u003e\u003ctable\u003e\u003ctr\u003e\u003ctd style=\"height:10px\"\u003e\u003c\/td\u003e\u003c\/tr\u003e\u003c\/table\u003e\u003c\/center\u003e\n\n\u003ccenter\u003e\u003ctable\u003e\u003ctr\u003e\u003ctd style=\"height:10px\"\u003e\u003c\/td\u003e\u003c\/tr\u003e\u003c\/table\u003e\u003c\/center\u003e\n\n\u003cdiv style=\"width:95%;padding-top:20px;padding-bottom:20px\"\u003e\n\n\u003cdiv style=\"text-align:left;font-size:16px;font-weight:bold;padding-bottom:20px\"\u003e GOODS SPECIFICS \u003c\/div\u003e\n\n\u003cdiv style=\"text-align:left;font-size:14px;line-height:1.6em;\"\u003e\n\n\u003cdiv style=\"width:100%;margin-bottom:5px;line-height:1.6em;font-size:14px\"\u003e - \u003cstrong\u003eDate of issue:\u003c\/strong\u003e July 5, 2024\u003c\/div\u003e\n\n\u003cdiv style=\"width:100%;margin-bottom:5px;line-height:1.6em;font-size:14px\"\u003e - \u003cstrong\u003ePages, weight, size:\u003c\/strong\u003e 172 pages | 360g | 170*225*11mm\u003c\/div\u003e\n\n\u003cdiv style=\"width:100%;margin-bottom:5px;line-height:1.6em;font-size:14px\"\u003e - \u003cstrong\u003eISBN13:\u003c\/strong\u003e 9791193926444 \u003c\/div\u003e\n\n\n\u003c\/div\u003e\n\n\n\u003c\/div\u003e\n\n\n\u003c\/div\u003e\n\n\u003ccenter\u003e\n\n\u003ccenter\u003e\u003ctable\u003e\u003ctr\u003e\u003ctd style=\"height:10px\"\u003e\u003c\/td\u003e\u003c\/tr\u003e\u003c\/table\u003e\u003c\/center\u003e\n\n\u003ccenter\u003e\u003ctable\u003e\u003ctr\u003e\u003ctd style=\"height:10px\"\u003e\u003c\/td\u003e\u003c\/tr\u003e\u003c\/table\u003e\u003c\/center\u003e\n\n\u003cspan\u003e\u003c\/span\u003e\n\n\u003c\/center\u003e\n\n\n\u003c\/center\u003e","brand":"LIBRAIRIE COREENNE","offers":[{"title":"Default Title","offer_id":43893688107050,"sku":"110183","price":28.0,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0683\/2750\/5962\/files\/166ca40e43255edd37672e8ef89d3cee.jpg?v=1765411850","url":"https:\/\/librairie.coreenne.fr\/en\/products\/110183","provider":"LIBRAIRIE COREENNE","version":"1.0","type":"link"}