{"id":121,"date":"2025-08-15T16:41:07","date_gmt":"2025-08-15T08:41:07","guid":{"rendered":"https:\/\/alyname.top\/index.php\/2025\/08\/15\/%e7%ac%94%e8%ae%b0-denoising-diffusion-probabilistic-models\/"},"modified":"2025-08-16T00:15:48","modified_gmt":"2025-08-15T16:15:48","slug":"denoising-diffusion-probabilistic-models","status":"publish","type":"post","link":"https:\/\/alyname.top\/index.php\/2025\/08\/15\/denoising-diffusion-probabilistic-models\/","title":{"rendered":"\u7b14\u8bb0 – Denoising Diffusion Probabilistic Models"},"content":{"rendered":"

\u554a\u2026\u2026\u53c8\u56de\u6765\u4e86\u2026\u2026\u719f\u6089\u7684 DDPM \u554a\u2026\u2026<\/p>\n

\u8fd9\u7bc7\u6587\u7ae0\u7684\u6838\u5fc3\u8d21\u732e\u5728\u4e8e\uff1a\u63d0\u51fa\u4e00\u79cd\u57fa\u4e8e\u591a\u8f6e \u52a0\u566a \/ \u53bb\u566a \u8fdb\u884c\u56fe\u50cf\u751f\u6210\u7684\u65b9\u6cd5\u6846\u67b6\u3002\u8fd9\u79cd\u65b9\u6cd5\u6846\u67b6\uff08Diffusion\uff09\u5728\u67d0\u79cd\u610f\u4e49\u4e0a\u72ec\u7acb\u4e8e\u6240\u91c7\u7528\u7684\u6a21\u578b\u5b58\u5728\uff1b\u6a21\u578b\u6240\u5b66\u4e60\u7684\u662f\u566a\u58f0\u2014\u2014\u5bf9\u67d0\u5f20\u5e26\u566a\u58f0\u56fe\u7247\u6765\u8bf4\uff0c\u566a\u58f0\u6700\u53ef\u80fd\u5728\u54ea\uff0c\u4e5f\u5373\u539f\u56fe\u6700\u53ef\u80fd\u957f\u5565\u6837\u5b50\u3002<\/p>\n

Diffusion \u524d\u6700\u6d41\u884c\u7684\u56fe\u50cf\u751f\u6210\u65b9\u6cd5\u662f GAN\uff08\u6807\u5fd7\u6027\u7684\u5de5\u4f5c\u5982 StyleGAN\uff09\uff0c\u6b21\u4e00\u4e9b\u7684\u6709 VAE\uff08\u53d8\u5206\u81ea\u7f16\u7801\u5668\uff09\u3001\u6d41\u65b9\u6cd5\u3001\u5404\u79cd\u81ea\u56de\u5f52\u6a21\u578b\u7b49\u7b49\uff0c\u4f46\u5b83\u4eec\u8bad\u7ec3\u6548\u7387\u5f80\u5f80\u6781\u4f4e\uff0c\u751f\u6210\u56fe\u7247\u7684\u8d28\u91cf\u4e5f\u4e0d\u5f88\u9ad8\uff08\u76f8\u5bf9\u4e8e Diffusion \u7cfb\u5217\u800c\u8a00\uff09\u3002DDPM \u4f5c\u4e3a\u6700\u65e9\u7684 Diffusion \u65b9\u6cd5\u4e4b\u4e00\u5e76\u975e\u5f88\u5f15\u4eba\u6ce8\u76ee\uff0c\u4f46\u7ecf\u8fc7\u51e0\u8f6e\u8bba\u6587\u5468\u671f\u5347\u7ea7\u800c\u6210\u7684 DDIM\u3001LDM \/ Stable Diffusion \u5f88\u5feb\u5c55\u73b0\u51fa Diffusion \u7cfb\u5217\u65b9\u6cd5\u7684\u6781\u9ad8\u6f5c\u529b\uff0c\u8fc5\u901f\u5e2d\u5377\u6574\u4e2a\u56fe\u50cf\u751f\u6210\u9886\u57df\u3002<\/p>\n

\n

\u5565\u662f VAE\uff1f\u53d8\u5206 \u81ea \u7f16\u7801\u5668\u3002<\/p>\n<\/blockquote>\n

\u8fd9\u91cc\u4e3b\u8981\u5173\u6ce8 DDPM \u7684\u6570\u5b66\u65b9\u6cd5\u53ca\u82e5\u5e72\u7ec6\u8282\u3002<\/p>\n

[2006.11239] Denoising Diffusion Probabilistic Models<\/a>\uff082020 \u5e74 6 \u6708\uff09<\/p>\n

\u770b\u8d77\u6765\u5f88\u5389\u5bb3\u7684\u535a\u5ba2 \u6269\u6563\u6a21\u578b\u4e4bDDPM – \u77e5\u4e4e<\/a><\/p>\n

\u6df1\u5165\u6d45\u51fa\u4e14\u5f0f\u5b50\u90fd\u5f88\u597d\u7406\u89e3\u7684\u535a\u5ba2 \u751f\u6210\u6269\u6563\u6a21\u578b\u6f2b\u8c08\uff08\u4e00\uff09\uff1aDDPM = \u62c6\u697c + \u5efa\u697c – \u79d1\u5b66\u7a7a\u95f4|Scientific Spaces<\/a><\/p>\n

\n

\"Pasted<\/p>\n

\u6269\u6563\u8fc7\u7a0b<\/h5>\n

Diffusion \u5305\u542b\u4e24\u4e2a\u76f8\u53cd\u7684\u8fc7\u7a0b\uff1a\u524d\u5411\u7684\u6269\u6563\u8fc7\u7a0b\u7ed9\u4e00\u5f20\u56fe\u7247\u52a0\u5165 <\/g><\/g><\/g><\/svg>T<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u6b21\u968f\u673a\u566a\u58f0\uff0c\u6700\u7ec8\u5c06\u5176\u53d8\u4e3a\u5b8c\u5168\u7684\u7eaf\u566a\u58f0\u56fe\uff0c\u8fd9\u4e2a\u8fc7\u7a0b\u4e3b\u8981\u7528\u4e8e\u8bad\u7ec3\u6a21\u578b\uff1b\u53cd\u5411\u7684\u53bb\u566a\u8fc7\u7a0b\u7ed9\u4e00\u4e2a\u7eaf\u566a\u58f0\u56fe\uff0c\u5229\u7528\u6a21\u578b\u9884\u6d4b <\/g><\/g><\/g><\/svg>T<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u6b21\u566a\u58f0\u5e76\u53bb\u566a\uff0c\u5f97\u5230\u4e00\u5f20\u6e05\u6670\u7684\u56fe\u7247\uff0c\u8fd9\u4e2a\u8fc7\u7a0b\u4e3b\u8981\u7528\u4e8e\u56fe\u7247\u751f\u6210\u3002<\/p>\n

\u52a0\u566a\u8fc7\u7a0b\u4e2d\uff0c\u7b2c <\/g><\/g><\/g><\/svg>t<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u6b65\u52a0\u5165\u65b9\u5dee\u4e3a <\/g><\/g><\/g><\/g><\/g><\/svg>\u03b2<\/mi>t<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u7684 Gaussian \u566a\u58f0<\/p>\n

<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>q<\/mi>(<\/mo>x<\/mi>t<\/mi><\/msub>|<\/mo>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>)<\/mo>=<\/mo>N<\/mi><\/mrow>(<\/mo>x<\/mi>t<\/mi><\/msub>;<\/mo>1<\/mn>\u2212<\/mo>\u03b2<\/mi>t<\/mi><\/msub><\/msqrt>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>,<\/mo>\u03b2<\/mi>t<\/mi><\/msub>I<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

\u4e0a\u5f0f\u542b\u4e49\uff1a\u7ed9\u5b9a\u7b2c <\/g><\/g><\/g><\/g><\/g><\/svg>t<\/mi>\u2212<\/mo>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container> \u6b65\u7684\u6570\u636e\u5206\u5e03 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>\u223c<\/mo>q<\/mi>(<\/mo>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u7b2c <\/g><\/g><\/g><\/svg>t<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u6b65 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>t<\/mi><\/mrow><\/msub>\u223c<\/mo>q<\/mi>(<\/mo>x<\/mi>t<\/mi><\/mrow><\/msub>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container> \u7684\u6570\u636e\u5206\u5e03\u7531\u5728\u524d\u4e00\u6b65\u7684\u6570\u636e\u4e0a\u52a0\u968f\u673a Gaussian \u566a\u58f0\u51b3\u5b9a\u3002<\/p>\n

\u5177\u4f53\u64cd\u4f5c\u662f<\/p>\n

<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>t<\/mi><\/msub>=<\/mo>1<\/mn>\u2212<\/mo>\u03b2<\/mi>t<\/mi><\/msub><\/msqrt>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>+<\/mo>\u03b2<\/mi>t<\/mi><\/msub><\/msqrt>\u03f5<\/mi>t<\/mi><\/msub>,<\/mo><\/mstyle>\u03f5<\/mi>t<\/mi><\/msub>\u223c<\/mo>N<\/mi><\/mrow>(<\/mo>0<\/mn>,<\/mo>I<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

\u6240\u6709 <\/g><\/g><\/g><\/g><\/g><\/svg>\u03b2<\/mi>t<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u88ab\u9884\u5148\u786e\u5b9a\u3002<\/p>\n

\n

\u4e3a\u4ec0\u4e48 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u8981\u4e58\u4e00\u4e2a <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>1<\/mn>\u2212<\/mo>\u03b2<\/mi>t<\/mi><\/msub><\/msqrt><\/math><\/mjx-assistive-mml><\/mjx-container>\uff1f\u56e0\u4e3a\u5e0c\u671b <\/g><\/g><\/g><\/svg>x<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u7684\u65b9\u5dee\u4e00\u76f4\u662f <\/g><\/g><\/g><\/svg>I<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u8fd9\u6837\u6700\u540e\u5f97\u5230\u7684\u566a\u58f0\u56fe\u63a5\u8fd1\u5f88\u7b80\u6d01\u7684 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>T<\/mi><\/msub>\u223c<\/mo>N<\/mi><\/mrow>(<\/mo>0<\/mn>,<\/mo>I<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\u3002<\/p>\n<\/blockquote>\n

\u4e00\u4e2a\u91cd\u8981\u7684\u4e8b\u5b9e\u662f\uff0c\u7531\u4e8e Gaussian \u5206\u5e03\u7684\u53ef\u52a0\u6027\uff0c<\/g><\/g><\/g><\/svg>t<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u6b65\u52a0\u566a\u53ef\u4ee5\u4e00\u5e76\u5b8c\u6210\u3002\u8bb0 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>\u03b1<\/mi>t<\/mi><\/msub>=<\/mo>1<\/mn>\u2212<\/mo>\u03b2<\/mi>t<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u63a8\u4e00\u4e0b\u5f97\u5230<\/p>\n

<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>t<\/mi><\/msub>=<\/mo>\u220f<\/mo>i<\/mi>=<\/mo>1<\/mn><\/mrow>t<\/mi><\/munderover>\u03b1<\/mi>i<\/mi><\/msub><\/msqrt>x<\/mi>0<\/mn><\/msub>+<\/mo>1<\/mn>\u2212<\/mo>\u220f<\/mo>i<\/mi>=<\/mo>1<\/mn><\/mrow>t<\/mi><\/munderover>\u03b1<\/mi>i<\/mi><\/msub><\/msqrt>\u03f5<\/mi>,<\/mo><\/mstyle>\u03f5<\/mi>\u223c<\/mo>N<\/mi><\/mrow>(<\/mo>0<\/mn>,<\/mo>I<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

\u518d\u8bb0 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>\u03b1<\/mi>\u00af<\/mo><\/mover><\/mrow>t<\/mi><\/msub>=<\/mo>\u220f<\/mo>i<\/mi>=<\/mo>1<\/mn><\/mrow>t<\/mi><\/munderover>\u03b1<\/mi>i<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u5219\u53ef\u4ee5\u7b80\u5355\u5730\u5199\u4f5c <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>t<\/mi><\/msub>=<\/mo>\u03b1<\/mi>\u00af<\/mo><\/mover><\/mrow>t<\/mi><\/msub><\/msqrt>x<\/mi>0<\/mn><\/msub>+<\/mo>1<\/mn>\u2212<\/mo>\u03b1<\/mi>\u00af<\/mo><\/mover><\/mrow>t<\/mi><\/msub><\/msqrt>\u03f5<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container>\u3002<\/p>\n

\u7136\u540e <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>0<\/mn><\/msub>\u223c<\/mo>q<\/mi>(<\/mo>x<\/mi>0<\/mn><\/msub>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container> \u4e5f\u770b\u4f5c\u65b9\u5dee\u4e3a <\/g><\/g><\/g><\/svg>0<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container> \u7684 Gaussian \u5206\u5e03 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>N<\/mi><\/mrow>(<\/mo>x<\/mi>0<\/mn><\/msub>,<\/mo>0<\/mn>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u8fd9\u6837 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>t<\/mi><\/msub>\u223c<\/mo>N<\/mi><\/mrow>(<\/mo>x<\/mi>t<\/mi><\/msub>;<\/mo>\u03b1<\/mi>\u00af<\/mo><\/mover><\/mrow>t<\/mi><\/msub><\/msqrt>x<\/mi>0<\/mn><\/msub>,<\/mo>1<\/mn>\u2212<\/mo>\u03b1<\/mi>\u00af<\/mo><\/mover><\/mrow>t<\/mi><\/msub>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\u3002\u8fd9\u5c31\u662f <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>q<\/mi>(<\/mo>x<\/mi>t<\/mi><\/msub>|<\/mo>x<\/mi>0<\/mn><\/msub>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\u3002<\/p>\n

\u7406\u60f3\u53bb\u566a\u8fc7\u7a0b<\/h5>\n

\u53bb\u566a\u8fc7\u7a0b\u4e2d\uff0c\u7b2c <\/g><\/g><\/g><\/svg>t<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u6b65\u53bb\u6389\u521a\u521a\u52a0\u4e0a\u7684\u968f\u673a\u53d8\u91cf\u2026\u2026<\/p>\n

\u7b49\u7b49\uff01\u968f\u673a\u53d8\u91cf\u600e\u4e48\u53ef\u80fd\u201c\u53bb\u6389\u201d\uff1f\u6bd5\u7adf\u6211\u4eec\u4e5f\u4e0d\u77e5\u9053\u5b83\u662f\u591a\u5c11\u554a\uff01\u5c31\u7b97\u6211\u4eec\u5c1d\u8bd5\u7528\u6a21\u578b\u53bb\u9884\u6d4b\u52a0\u566a\u8fc7\u7a0b\u7b2c <\/g><\/g><\/g><\/svg>t<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u6b65\u52a0\u7684 <\/g><\/g><\/g><\/g><\/g><\/svg>\u03f5<\/mi>t<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u957f\u5565\u6837\uff0c\u6700\u540e\u4e5f\u53ea\u4f1a\u8bad\u51fa\u4e00\u4e2a\u53ea\u8f93\u51fa Gaussian \u566a\u58f0\u7684\u6a21\u578b\uff08\u56e0\u4e3a\u5f53\u65f6\u52a0\u4e0a\u7684\u5c31\u662f\u4e00\u4e2a Gaussian \u5206\u5e03\u7684\u968f\u673a\u53d8\u91cf\uff09\u2026\u2026<\/p>\n

\u4e0d\u7ba1\u600e\u6837\uff0c\u7531\u4e8e Gaussian \u5206\u5e03\u7684\u53ef\u52a0\u6027\uff0c\u6211\u4eec\u77e5\u9053 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u80af\u5b9a\u670d\u4ece\u67d0\u4e2a Gaussian \u5206\u5e03\u3002<\/p>\n

\u6765\u4e00\u4e2a Bayes\uff1a<\/p>\n

<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>q<\/mi>(<\/mo>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>|<\/mo>x<\/mi>t<\/mi><\/msub>,<\/mo>x<\/mi>0<\/mn><\/msub>)<\/mo>=<\/mo>q<\/mi>(<\/mo>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>|<\/mo>x<\/mi>0<\/mn><\/msub>)<\/mo><\/mrow>q<\/mi>(<\/mo>x<\/mi>t<\/mi><\/msub>|<\/mo>x<\/mi>0<\/mn><\/msub>)<\/mo><\/mrow><\/mfrac>q<\/mi>(<\/mo>x<\/mi>t<\/mi><\/msub>|<\/mo>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

\n

\u4e3a\u5565\u8981\u518d\u8003\u8651 <\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>0<\/mn><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container>\uff1f\u56e0\u4e3a <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u662f\u7531 <\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>0<\/mn><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u751f\u6210\u7684\uff0c\u6ca1\u6709\u5355\u72ec\u7684 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>q<\/mi>(<\/mo>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u6216\u8005\u8bf4\uff0c\u5f53\u6211\u4eec\u5199\u51fa <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>q<\/mi>(<\/mo>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container> \u65f6\uff0c\u5176\u5b9e\u5c31\u81ea\u5e26\u4e3a <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>q<\/mi>(<\/mo>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>|<\/mo>x<\/mi>0<\/mn><\/msub>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container> \u4e86\u3002<\/p>\n

\u6216\u8005\u8bf4\uff0c\u8fd9\u91cc\u8ba8\u8bba\u7684\u662f\u7406\u60f3\u53bb\u566a\u8fc7\u7a0b\uff0c\u5728\u4ec5\u77e5\u9053\u4e00\u5f20\u566a\u58f0\u56fe <\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>t<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container>\uff08\u800c\u4e0d\u77e5\u9053\u539f\u56fe\u53ef\u80fd\u6709\u54ea\u4e9b\uff09\u7684\u60c5\u51b5\u4e0b\u5f53\u7136\u4e0d\u53ef\u80fd\u7406\u60f3\u5730\u6062\u590d\u539f\u56fe\u3002<\/p>\n

\u6a21\u578b\u5230\u65f6\u5019\u4f1a\u5728\u56fe\u7247\u96c6\u4e0a\u8bad\u7ec3\uff0c\u5c1d\u8bd5\u505a\u5230\u4ec5\u6839\u636e\u8f93\u5165\u7684 <\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>t<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u6062\u590d\u539f\u56fe\u3002\u6211\u4eec\u628a\u8fd9\u4e2a\u8fc7\u7a0b\u8bb0\u4f5c\u6a21\u578b\u53bb\u566a\u8fc7\u7a0b<\/strong> <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>p<\/mi>\u03b8<\/mi><\/msub>(<\/mo>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>|<\/mo>x<\/mi>t<\/mi><\/msub>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u4ee5\u4e0e\u7406\u60f3\u53bb\u566a\u8fc7\u7a0b<\/strong>\u533a\u5206\u3002<\/p>\n

\u90a3\u4e3a\u5565\u6700\u540e\u90a3\u9879\u6ca1\u6709 <\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>0<\/mn><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container>\uff1f\u5e26\u4e0a\u4e5f\u884c\uff0c\u4f46\u7531 Markov \u94fe\u7684\u539f\u56e0\uff0c<\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>t<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u53ea\u548c <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u76f8\u5173\u6240\u4ee5\u591a\u6b64\u4e00\u4e3e\u3002<\/p>\n<\/blockquote>\n

\uff08\u73b0\u5728\u6211\u8fd8\u4e0d\u77e5\u9053\u8981\u5e72\u5565\u2026\u2026\u4f46\u53ef\u4ee5\u628a\u524d\u9762\u7684\u4e1c\u897f\u4ee3\u8fdb\u6765\u6240\u4ee5\u5c31\u4ee3\u5427\uff09<\/p>\n

\u5229\u7528 Gaussian \u5206\u5e03\u7684\u5bc6\u5ea6\u51fd\u6570\uff08\u7701\u7565 <\/g><\/g><\/g><\/svg>exp<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u524d\u7684\u5e38\u6570\u9879\uff09<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>exp<\/mi>\u2061<\/mo>(<\/mo>\u2212<\/mo>(<\/mo>x<\/mi>\u2212<\/mo>\u03bc<\/mi>)<\/mo>2<\/mn><\/msup><\/mrow>2<\/mn>\u03c3<\/mi>2<\/mn><\/msup><\/mrow><\/mfrac>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container> \u4ee3\u5165\u4e4b\u524d\u7ed3\u679c\uff1a<\/p>\n

<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>q<\/mi>(<\/mo>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>|<\/mo>x<\/mi>t<\/mi><\/msub>,<\/mo>x<\/mi>0<\/mn><\/msub>)<\/mo><\/mtd>=<\/mo>exp<\/mi>\u2061<\/mo>(<\/mo>\u2212<\/mo>1<\/mn>2<\/mn><\/mfrac>(<\/mo>(<\/mo>x<\/mi>t<\/mi><\/msub>\u2212<\/mo>\u03b1<\/mi><\/msqrt>t<\/mi><\/msub>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>)<\/mo>2<\/mn><\/msup><\/mrow>1<\/mn>\u2212<\/mo>\u03b1<\/mi>t<\/mi><\/msub><\/mrow><\/mfrac>\u2212<\/mo>(<\/mo>x<\/mi>t<\/mi><\/msub>\u2212<\/mo>\u03b1<\/mi>\u00af<\/mo><\/mover><\/mrow>t<\/mi><\/msub><\/msqrt>x<\/mi>0<\/mn><\/msub>)<\/mo>2<\/mn><\/msup><\/mrow>1<\/mn>\u2212<\/mo>\u03b1<\/mi>\u00af<\/mo><\/mover><\/mrow>t<\/mi><\/msub><\/mrow><\/mfrac>+<\/mo>(<\/mo>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>\u2212<\/mo>\u03b1<\/mi>\u00af<\/mo><\/mover><\/mrow>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub><\/msqrt>x<\/mi>0<\/mn><\/msub>)<\/mo>2<\/mn><\/msup><\/mrow>1<\/mn>\u2212<\/mo>\u03b1<\/mi>\u00af<\/mo><\/mover><\/mrow>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub><\/mrow><\/mfrac>)<\/mo>)<\/mo><\/mtd><\/mtr>=<\/mo>exp<\/mi>\u2061<\/mo>(<\/mo>\u2212<\/mo>1<\/mn>2<\/mn><\/mfrac>(<\/mo>(<\/mo>\u03b1<\/mi>t<\/mi><\/msub>1<\/mn>\u2212<\/mo>\u03b1<\/mi>t<\/mi><\/msub><\/mrow><\/mfrac>+<\/mo>1<\/mn>1<\/mn>\u2212<\/mo>\u03b1<\/mi>\u00af<\/mo><\/mover><\/mrow>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub><\/mrow><\/mfrac>)<\/mo>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow>2<\/mn><\/msubsup>\u2212<\/mo>(<\/mo>2<\/mn>\u03b1<\/mi><\/msqrt>t<\/mi><\/msub>x<\/mi>t<\/mi><\/msub><\/mrow>1<\/mn>\u2212<\/mo>\u03b1<\/mi>t<\/mi><\/msub><\/mrow><\/mfrac>+<\/mo>2<\/mn>\u03b1<\/mi>\u00af<\/mo><\/mover><\/mrow>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub><\/msqrt>x<\/mi>0<\/mn><\/msub><\/mrow>1<\/mn>\u2212<\/mo>\u03b1<\/mi>\u00af<\/mo><\/mover><\/mrow>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub><\/mrow><\/mfrac>)<\/mo>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>+<\/mo>c<\/mi>)<\/mo>)<\/mo><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

\u540e\u9762 <\/g><\/g><\/g><\/svg>c<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u662f\u4e00\u5768\u5e38\u6570\u3002\u9274\u4e8e\u4e4b\u524d\u5df2\u7ecf\u7701\u7565\u5e38\u6570\u9879\u4e86\uff0c\u5e76\u4e14\u5927\u5bb6\u63a8\u5230\u8fd9\u7684\u65f6\u5019\u4e5f\u81ea\u52a8\u7701\u7565 <\/g><\/g><\/g><\/svg>c<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u4e86\u6211\u4eec\u4e5f\u5c31\u4e0d\u7ba1\u5b83\u4e86\u3002<\/p>\n

\u4e3a\u4ec0\u4e48\u8981\u5316\u6210\u8fd9\u6837\uff1f\u56e0\u4e3a\u6211\u4eec\u5df2\u7ecf\u77e5\u9053\uff0c<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u670d\u4ece\u67d0\u4e2a Gaussian \u5206\u5e03\uff0c\u5316\u6210\u4e0a\u9762\u7684\u6837\u5b50\u518d\u914d\u65b9\u4e00\u4e0b\u53ef\u4ee5\u628a\u8fd9\u4e2a Gaussian \u5206\u5e03\u7684\u5747\u503c <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>\u03bc<\/mi>~<\/mo><\/mover><\/mrow>t<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u548c\u65b9\u5dee <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>\u03b2<\/mi>~<\/mo><\/mover><\/mrow>t<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u6c42\u51fa\u6765\u3002\u5b83\u4eec\u662f\uff1a<\/p>\n

<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>\u03bc<\/mi>~<\/mo><\/mover><\/mrow>t<\/mi><\/msub><\/mtd>=<\/mo>\u03b1<\/mi>t<\/mi><\/msub><\/msqrt>1<\/mn>\u2212<\/mo>\u03b1<\/mi>\u00af<\/mo><\/mover><\/mrow>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub><\/mrow>1<\/mn>\u2212<\/mo>\u03b1<\/mi>\u00af<\/mo><\/mover><\/mrow>t<\/mi><\/msub><\/mrow><\/mfrac>x<\/mi>t<\/mi><\/msub>+<\/mo>\u03b1<\/mi>\u00af<\/mo><\/mover><\/mrow>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub><\/msqrt>1<\/mn>\u2212<\/mo>\u03b1<\/mi>t<\/mi><\/msub><\/mrow>1<\/mn>\u2212<\/mo>\u03b1<\/mi>\u00af<\/mo><\/mover><\/mrow>t<\/mi><\/msub><\/mrow><\/mfrac>x<\/mi>0<\/mn><\/msub><\/mtd><\/mtr>\u03b2<\/mi>~<\/mo><\/mover><\/mrow>t<\/mi><\/msub><\/mtd>=<\/mo>(<\/mo>1<\/mn>\u2212<\/mo>\u03b1<\/mi>\u00af<\/mo><\/mover><\/mrow>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>)<\/mo>(<\/mo>1<\/mn>\u2212<\/mo>\u03b1<\/mi>t<\/mi><\/msub>)<\/mo><\/mrow>1<\/mn>\u2212<\/mo>\u03b1<\/mi>\u00af<\/mo><\/mover><\/mrow>t<\/mi><\/msub><\/mrow><\/mfrac><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

\u6ce8\u610f\u5230\u65b9\u5dee\u662f\u4e00\u4e2a\u5e38\u6570\uff0c\u8fd9\u662f\u81ea\u7136\u7684\u3002\u5747\u503c\u5219\u662f\u4e00\u4e2a\u5173\u4e8e <\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>t<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u548c <\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>0<\/mn><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u7684\u51fd\u6570\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u5728\u7406\u60f3\u53bb\u566a\u8fc7\u7a0b\u4e2d\uff0c\u6211\u4eec\u5728\u77e5\u9053 <\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>0<\/mn><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u7684\u60c5\u51b5\u4e0b\uff0c\u53ef\u4ee5\u8fd9\u6837\u6839\u636e <\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>t<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u5f04\u51fa\u4e00\u4e2a\u5206\u5e03\uff0c\u7136\u540e\u91c7\u6837 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container>\u3002<\/p>\n

\u6a21\u578b\u53bb\u566a\u8fc7\u7a0b<\/h5>\n

\u5bf9 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>p<\/mi>\u03b8<\/mi><\/mrow><\/msub>(<\/mo>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>|<\/mo>x<\/mi>t<\/mi><\/msub>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container> \u5462\uff1f\u6211\u4eec\u5e0c\u671b\u5b83\u4e0e <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>q<\/mi>(<\/mo>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>|<\/mo>x<\/mi>t<\/mi><\/msub>,<\/mo>x<\/mi>0<\/mn><\/msub>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container> \u8d8a\u63a5\u8fd1\u8d8a\u597d\u3002\u8bbe <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>p<\/mi>\u03b8<\/mi><\/msub>(<\/mo>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>|<\/mo>x<\/mi>t<\/mi><\/msub>)<\/mo>=<\/mo>N<\/mi><\/mrow>(<\/mo>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>;<\/mo>\u03bc<\/mi>\u03b8<\/mi><\/msub>(<\/mo>x<\/mi>t<\/mi><\/msub>,<\/mo>t<\/mi>)<\/mo>,<\/mo>\u03a3<\/mi>\u03b8<\/mi><\/msub>(<\/mo>t<\/mi>)<\/mo>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u7531\u4e4b\u524d\u7684\u8ba8\u8bba\u65b9\u5dee\u662f\u4e2a\u5e38\u6570\uff0c\u6240\u4ee5\u53ef\u4ee5\u4e0d\u8ba9\u6a21\u578b\u7ba1\u8fd9\u4e9b\uff0c<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>\u03a3<\/mi>\u03b8<\/mi><\/msub>(<\/mo>t<\/mi>)<\/mo>=<\/mo>\u03b2<\/mi>~<\/mo><\/mover><\/mrow>t<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container>\u3002<\/p>\n

\u8861\u91cf\u4e24\u4e2a\u5206\u5e03\u7684\u201c\u63a5\u8fd1\u7a0b\u5ea6\u201d\u6709 KL \u6563\u5ea6\uff0c\u6211\u4eec\u8ba1\u7b97 <\/g><\/g><\/g><\/g><\/g><\/svg>p<\/mi>\u03b8<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u548c <\/g><\/g><\/g><\/svg>q<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u7684 KL \u6563\u5ea6\u770b\u770b\u8981\u4f18\u5316\u7684\u76ee\u6807\u662f\u5565\uff1a<\/p>\n

<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>D<\/mi>K<\/mi>L<\/mi><\/mrow><\/msub>(<\/mo>q<\/mi>\u2225<\/mo>p<\/mi>\u03b8<\/mi><\/msub>)<\/mo>=<\/mo>1<\/mn>2<\/mn><\/mfrac>(<\/mo>1<\/mn>\u03b2<\/mi>~<\/mo><\/mover><\/mrow>t<\/mi><\/msub><\/mfrac>\u2225<\/mo>\u03bc<\/mi>~<\/mo><\/mover><\/mrow>t<\/mi><\/msub>(<\/mo>x<\/mi>t<\/mi><\/msub>,<\/mo>x<\/mi>0<\/mn><\/msub>)<\/mo>\u2212<\/mo>\u03bc<\/mi>\u03b8<\/mi><\/msub>(<\/mo>x<\/mi>t<\/mi><\/msub>,<\/mo>t<\/mi>)<\/mo>\u2225<\/mo>2<\/mn><\/msup>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

\n

KL \u6563\u5ea6\uff08Kullback-Leibler Divergence\uff09\u662f\u8861\u91cf\u4e24\u4e2a\u5206\u5e03\u4e4b\u95f4\u5dee\u5f02\u7684\u65b9\u6cd5\uff0c\u5e7f\u6cdb\u8fd0\u7528\u4e8e\u673a\u5668\u5b66\u4e60\u7b49\u9886\u57df\u3002\u5b83\u6709\u4e00\u4e2a\u4e0d\u90a3\u4e48\u552c\u4eba\u7684\u540d\u5b57\u53eb\u201c\u76f8\u5bf9\u71b5\u201d\u3002<\/p>\n

<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>D<\/mi>K<\/mi>L<\/mi><\/mrow><\/msub>(<\/mo>P<\/mi>\u2225<\/mo>Q<\/mi>)<\/mo>=<\/mo>\u222b<\/mo>x<\/mi><\/msub>P<\/mi>(<\/mo>x<\/mi>)<\/mo>log<\/mi>\u2061<\/mo>P<\/mi>(<\/mo>x<\/mi>)<\/mo><\/mrow>Q<\/mi>(<\/mo>x<\/mi>)<\/mo><\/mrow><\/mfrac>d<\/mi>x<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/p><\/blockquote>\n

\n

\u6ce8\u610f\u5230\u8fd9\u4e2a\u5f0f\u5b50\u662f\u4e0d\u5bf9\u79f0<\/strong>\u7684\uff01\uff01\u5176\u4e2d\uff0c<\/g><\/g><\/g><\/svg>P<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u662f\u771f\u5b9e\u5206\u5e03\uff0c<\/g><\/g><\/g><\/svg>Q<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u662f\u8fd1\u4f3c\u5206\u5e03\u3002<\/p>\n

\u5bf9\u4e24\u4e2a Gaussian \u5206\u5e03\u6765\u8bf4\uff0cKL \u6563\u5ea6\u53ef\u4ee5\u7528\u4ee5\u4e0b\u5f0f\u5b50\u8ba1\u7b97\uff1a<\/p>\n

<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>K<\/mi>L<\/mi>(<\/mo>p<\/mi>1<\/mn><\/msub>\u2225<\/mo>p<\/mi>2<\/mn><\/msub>)<\/mo>=<\/mo>1<\/mn>2<\/mn><\/mfrac>(<\/mo>tr<\/mtext>(<\/mo>\u03a3<\/mi>2<\/mn>\u2212<\/mo>1<\/mn><\/mrow><\/msubsup>\u03a3<\/mi>1<\/mn><\/msub>)<\/mo>+<\/mo>(<\/mo>\u03bc<\/mi>2<\/mn><\/msub>\u2212<\/mo>\u03bc<\/mi>1<\/mn><\/msub>)<\/mo>T<\/mi><\/msup>\u03a3<\/mi>2<\/mn>\u2212<\/mo>1<\/mn><\/mrow><\/msubsup>(<\/mo>\u03bc<\/mi>2<\/mn><\/msub>\u2212<\/mo>\u03bc<\/mi>1<\/mn><\/msub>)<\/mo>\u2212<\/mo>n<\/mi>+<\/mo>log<\/mi>\u2061<\/mo>det<\/mo>\u03a3<\/mi>2<\/mn><\/msub><\/mrow>det<\/mo>\u03a3<\/mi>1<\/mn><\/msub><\/mrow><\/mfrac>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/p><\/blockquote>\n

\n

\u597d\u96be\u63a8\u2026\u2026ML \u7814\u7a76\u7684\u6570\u5b66\u7206\u7b97\u6d53\u5ea6\u8fd9\u4e48\u9ad8\u5417\u2026\u2026<\/p>\n

\u65e0\u8bba\u5982\u4f55\uff0c\u4e0a\u9762 <\/g><\/g><\/g><\/g><\/g><\/svg>p<\/mi>\u03b8<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u548c <\/g><\/g><\/g><\/svg>q<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u7684 KL \u6563\u5ea6\u5c31\u662f\u76f4\u63a5\u4ee3\u5165\u4e0a\u5f0f\u7684\u7ed3\u679c\u3002<\/p>\n<\/blockquote>\n

\u628a\u8fd9\u4e2a\u4f5c\u4e3a\u4f18\u5316\u76ee\u6807\u5c31\u884c\u5566\u3002<\/p>\n

<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>L<\/mi>=<\/mo>E<\/mi><\/mrow>q<\/mi>(<\/mo>x<\/mi>t<\/mi><\/msub>|<\/mo>x<\/mi>0<\/mn><\/msub>)<\/mo><\/mrow><\/msub>[<\/mo>1<\/mn>2<\/mn>\u03b2<\/mi>~<\/mo><\/mover><\/mrow>t<\/mi><\/msub><\/mrow><\/mfrac>\u2225<\/mo>\u03bc<\/mi>~<\/mo><\/mover><\/mrow>t<\/mi><\/msub>(<\/mo>x<\/mi>t<\/mi><\/msub>,<\/mo>x<\/mi>0<\/mn><\/msub>)<\/mo>\u2212<\/mo>\u03bc<\/mi>\u03b8<\/mi><\/msub>(<\/mo>x<\/mi>t<\/mi><\/msub>,<\/mo>t<\/mi>)<\/mo>\u2225<\/mo>2<\/mn><\/msup>]<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

\u4f46\u662f\u4f46\u662f\uff01DDPM \u53d1\u73b0\u8fd9\u6837\u6548\u679c\u4e0d\u597d\uff0c\u56e0\u6b64\u5b9e\u9645\u4e0d\u662f\u8fd9\u6837\u5e72\u7684\u3002\u4e4b\u524d\u5f97\u5230\u4e00\u4e2a\u8fd9\u6837\u7684\u5f0f\u5b50\uff1a<\/p>\n

<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>t<\/mi><\/msub>=<\/mo>\u03b1<\/mi>\u00af<\/mo><\/mover><\/mrow>t<\/mi><\/msub><\/msqrt>x<\/mi>0<\/mn><\/msub>+<\/mo>1<\/mn>\u2212<\/mo>\u03b1<\/mi>\u00af<\/mo><\/mover><\/mrow>t<\/mi><\/msub><\/msqrt>\u03f5<\/mi>,<\/mo><\/mstyle>\u03f5<\/mi>\u223c<\/mo>N<\/mi><\/mrow>(<\/mo>0<\/mn>,<\/mo>I<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

\u5728\u5df2\u77e5 <\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>t<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u7684\u60c5\u51b5\u4e0b\uff0c\u53ef\u4ee5\u7528 <\/g><\/g><\/g><\/svg>\u03f5<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u628a <\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>0<\/mn><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u6362\u6389\uff01\u8fd9\u4e2a\u505a\u6cd5\u88ab\u79f0\u4e3a\u91cd\u53c2\u6570\u5316\u3002\u628a\u4e0a\u9762\u7684 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>\u03bc<\/mi>~<\/mo><\/mover><\/mrow>t<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u5c55\u5f00\uff0c\u7136\u540e\u6362\u6389 <\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>0<\/mn><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u5f97\u5230<\/p>\n

<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>L<\/mi>=<\/mo>E<\/mi><\/mrow>[<\/mo>1<\/mn>2<\/mn>\u03b2<\/mi>~<\/mo><\/mover><\/mrow>t<\/mi><\/msub><\/mrow><\/mfrac>\u2225<\/mo>1<\/mn>\u03b1<\/mi>t<\/mi><\/msub><\/msqrt><\/mfrac>(<\/mo>x<\/mi>t<\/mi><\/msub>\u2212<\/mo>1<\/mn>\u2212<\/mo>\u03b1<\/mi>t<\/mi><\/msub><\/mrow>1<\/mn>\u2212<\/mo>\u03b1<\/mi>\u00af<\/mo><\/mover><\/mrow>t<\/mi><\/msub><\/msqrt><\/mfrac>\u03f5<\/mi>)<\/mo>\u2212<\/mo>\u03bc<\/mi>\u03b8<\/mi><\/msub>(<\/mo>x<\/mi>t<\/mi><\/msub>,<\/mo>t<\/mi>)<\/mo>\u2225<\/mo>2<\/mn><\/msup>]<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

\u5bf9 <\/g><\/g><\/g><\/g><\/g><\/svg>\u03bc<\/mi>\u03b8<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u4e5f\u8fdb\u884c\u91cd\u53c2\u6570\u5316<\/p>\n

<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>\u03bc<\/mi>\u03b8<\/mi><\/msub>=<\/mo>1<\/mn>\u03b1<\/mi>t<\/mi><\/msub><\/msqrt><\/mfrac>(<\/mo>x<\/mi>t<\/mi><\/msub>\u2212<\/mo>1<\/mn>\u2212<\/mo>\u03b1<\/mi>t<\/mi><\/msub><\/mrow>1<\/mn>\u2212<\/mo>\u03b1<\/mi>\u00af<\/mo><\/mover><\/mrow>t<\/mi><\/msub><\/msqrt><\/mfrac>\u03f5<\/mi>\u03b8<\/mi><\/msub>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

\u73b0\u5728\u4e0d\u8ba9\u6a21\u578b\u9884\u6d4b <\/g><\/g><\/g><\/svg>\u03bc<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u800c\u662f\u9884\u6d4b <\/g><\/g><\/g><\/svg>\u03f5<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u628a\u4e0a\u9762\u7684\u4e1c\u897f\u4e22\u5230 <\/g><\/g><\/g><\/svg>L<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u91cc\u5f97\u5230<\/p>\n

<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>L<\/mi>=<\/mo>E<\/mi><\/mrow>[<\/mo>(<\/mo>1<\/mn>\u2212<\/mo>\u03b1<\/mi>t<\/mi><\/msub>)<\/mo>2<\/mn><\/msup><\/mrow>2<\/mn>\u03b2<\/mi>~<\/mo><\/mover><\/mrow>t<\/mi><\/msub>\u03b1<\/mi>t<\/mi><\/msub>(<\/mo>1<\/mn>\u2212<\/mo>\u03b1<\/mi>\u00af<\/mo><\/mover><\/mrow>t<\/mi><\/msub>)<\/mo><\/mrow><\/mfrac>\u2225<\/mo>\u03f5<\/mi>\u2212<\/mo>\u03f5<\/mi>\u03b8<\/mi><\/msub>(<\/mo>x<\/mi>t<\/mi><\/msub>,<\/mo>t<\/mi>)<\/mo>\u2225<\/mo>2<\/mn><\/msup>]<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

\u518d\u6b21\u5730\uff0c\u4e0d\u7ba1\u524d\u9762\u90a3\u4e00\u5768\u5e38\u6570\uff0c\u5f97\u5230\u6700\u7ec8\u7684\u4f18\u5316\u76ee\u6807\uff1a<\/p>\n

<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>L<\/mi>=<\/mo>E<\/mi><\/mrow>[<\/mo>\u2225<\/mo>\u03f5<\/mi>\u2212<\/mo>\u03f5<\/mi>\u03b8<\/mi><\/msub>(<\/mo>x<\/mi>t<\/mi><\/msub>,<\/mo>t<\/mi>)<\/mo>\u2225<\/mo>2<\/mn><\/msup>]<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

\u771f\u597d\u3002<\/p>\n

\n

\u6240\u4ee5\u8fd8\u662f\u8981\u9884\u6d4b\u566a\u58f0\uff0c\u4f46\u566a\u58f0\u4e0d\u662f\u4e00\u4e2a\u6ee1\u8db3 Gaussian \u5206\u5e03\u7684\u968f\u673a\u53d8\u91cf\u5417\uff1f<\/p>\n

\u8003\u8651 <\/g><\/g><\/g><\/svg>\u03f5<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u7684\u610f\u4e49\uff1a\u6bcf\u6b21\u62ff\u4e00\u5f20\u56fe\u7247\u8bad\u7ec3\u65f6\u5bf9 <\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>0<\/mn><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u52a0 <\/g><\/g><\/g><\/svg>t<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u6b65\u566a\u58f0\u4e4b\u540e\u5f97\u5230 <\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>t<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u8fd9 <\/g><\/g><\/g><\/svg>t<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u6b65\u566a\u58f0\u7ec4\u5408\u5728\u4e00\u8d77\u662f <\/g><\/g><\/g><\/svg>\u03f5<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container>\u3002\u867d\u7136\u5206\u5e03 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>p<\/mi>(<\/mo>\u03f5<\/mi>|<\/mo>x<\/mi>t<\/mi><\/msub>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container> \u786e\u5b9e\u662f\u4e00\u4e2a Gaussian \u5206\u5e03\uff0c\u4f46\u5728\u5df2\u77e5 <\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>0<\/mn><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u7684\u60c5\u51b5\u4e0b <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>p<\/mi>(<\/mo>\u03f5<\/mi>|<\/mo>x<\/mi>t<\/mi><\/msub>,<\/mo>x<\/mi>0<\/mn><\/msub>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container> \u6240\u5305\u542b\u7684\u4fe1\u606f\u91cf\u7b49\u4ef7\u4e8e <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>q<\/mi>(<\/mo>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>|<\/mo>x<\/mi>t<\/mi><\/msub>,<\/mo>x<\/mi>0<\/mn><\/msub>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5373\uff0c\u5728\u5df2\u77e5 <\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>t<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u548c\u539f\u59cb\u56fe\u7247\u96c6\u7684\u60c5\u51b5\u4e0b\uff0c\u9884\u6d4b\u566a\u58f0\u4e0e\u9884\u6d4b\u52a0\u566a\u4e4b\u524d\u7684\u56fe\u7247\u7b49\u4ef7\u3002<\/p>\n<\/blockquote>\n

\n

\u603b\u611f\u89c9\u8bba\u6587\u4f5c\u8005\u7684\u5b9e\u9645\u60c5\u51b5\u662f\u5148\u62cd\u8111\u888b\u60f3\u51fa\u4e86\u8fd9\u4e2a\u4f18\u5316\u76ee\u6807\uff0c\u7136\u540e\u6839\u636e KL \u6563\u5ea6\u548c\u4e4b\u524d VAE \u5de5\u4f5c\u7684\u8303\u5f0f\u8bc1\u660e\u4e86\u5b83\u7684\u6b63\u786e\u6027\u2026\u2026<\/p>\n

\u6bd5\u7adf\u5176\u4e2d\u6709\u5927\u91cf\u201c\u820d\u5f03\u5e38\u6570\u201d\u7684\u64cd\u4f5c\uff0c\u5982\u679c\u4ec5\u5173\u6ce8\u5173\u952e\u53d8\u91cf\u7684\u6d41\u5411\u7684\u8bdd\uff0c\u5bf9 <\/g><\/g><\/g><\/svg>\u03f5<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u7684 <\/g><\/g><\/g><\/g><\/g><\/svg>L<\/mi>2<\/mn><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u8bef\u5dee\u3001\u5bf9 <\/g><\/g><\/g><\/svg>\u03bc<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u7684 <\/g><\/g><\/g><\/g><\/g><\/svg>L<\/mi>2<\/mn><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u8bef\u5dee\u548c\u5bf9\u539f\u59cb Gaussian \u5206\u5e03\u7684 KL \u6563\u5ea6\u8fd9\u4e09\u4e2a\u76ee\u6807\u5728\u76f4\u89c2\u4e0a\u770b\u662f\u6781\u4e3a\u76f8\u4f3c\u7684\u3002<\/p>\n<\/blockquote>\n

\u56de\u987e\u4e00\u4e0b\u8fd9\u4e32\u63a8\u5bfc\u90fd\u5728\u5e72\u5565\uff0c\u6bd5\u7adf\u6211\u4eec\u4f3c\u4e4e\u53ea\u662f\u4ece\u4e00\u5806\u663e\u7136\u7684\u4e8b\u5b9e\u63a8\u51fa\u4e86\u53e6\u4e00\u4e9b\u663e\u7136\u7684\u4e8b\u5b9e\uff1a<\/p>\n

    \n
  • \u9996\u5148\u5df2\u77e5 <\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>t<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u548c <\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>0<\/mn><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u7684\u8bdd\uff08\u7406\u60f3\u60c5\u5f62\uff09\u53ef\u4ee5\u63a8\u51fa <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5bf9 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u7684\u5206\u5e03\u6709\u4e00\u4e2a\u63cf\u8ff0\uff1b<\/li>\n
  • \u4f46\u56fe\u7247\u751f\u6210\u7684\u65f6\u5019\u80af\u5b9a\u4e0d\u80fd\u77e5\u9053 <\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>0<\/mn><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u56e0\u6b64\u5e0c\u671b\u6a21\u578b\u57fa\u4e8e <\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>t<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u9884\u6d4b\u7684 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u5206\u5e03\u548c\u7406\u60f3\u60c5\u5f62\u7684 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u5206\u5e03\u8d8a\u63a5\u8fd1\u8d8a\u597d\uff0c\u8fd9\u662f\u6211\u4eec\u7684\u539f\u59cb\u4f18\u5316\u76ee\u6807\uff0c\u4f46\u8fd9\u4e2a\u663e\u7136\u6ca1\u6cd5\u7b97\uff1b<\/li>\n
  • \u6211\u4eec\u7528\u7206\u7b97\u8bc1\u660e\u4e86\u8fd9\u4e09\u4e2a\u4f18\u5316\u76ee\u6807\u5728\u5ffd\u7565\u5e38\u6570\u7684\u60c5\u51b5\u4e0b\u7b49\u4ef7<\/strong>\uff1a\n
      \n
    • \uff08VAE \u7684\u89c2\u70b9\uff09<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>p<\/mi>\u03b8<\/mi><\/msub>(<\/mo>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>|<\/mo>x<\/mi>t<\/mi><\/msub>,<\/mo>t<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container> \u548c <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>q<\/mi>(<\/mo>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>|<\/mo>x<\/mi>t<\/mi><\/msub>,<\/mo>x<\/mi>0<\/mn><\/msub>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container> \u7684 KL \u6563\u5ea6\uff1b<\/li>\n
    • \uff08\u57fa\u4e8e\u56fe\u7247\u7684\u8bef\u5dee\uff09<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>\u03bc<\/mi>\u03b8<\/mi><\/msub>(<\/mo>x<\/mi>t<\/mi><\/msub>,<\/mo>t<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container> \u548c <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>\u03bc<\/mi>~<\/mo><\/mover><\/mrow>(<\/mo>x<\/mi>t<\/mi><\/msub>,<\/mo>x<\/mi>0<\/mn><\/msub>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container> \u7684 <\/g><\/g><\/g><\/g><\/g><\/svg>L<\/mi>2<\/mn><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u8bef\u5dee\uff1b<\/li>\n
    • \uff08\u57fa\u4e8e\u566a\u58f0\u7684\u8bef\u5dee\uff09<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>\u03f5<\/mi>\u03b8<\/mi><\/msub>(<\/mo>x<\/mi>t<\/mi><\/msub>,<\/mo>t<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container> \u548c <\/g><\/g><\/g><\/svg>\u03f5<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u7684 <\/g><\/g><\/g><\/g><\/g><\/svg>L<\/mi>2<\/mn><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u8bef\u5dee\u3002<\/li>\n<\/ul>\n<\/li>\n
    • \u7136\u540e\u53d1\u73b0\u6700\u540e\u4e00\u4e2a\u4f18\u5316\u76ee\u6807\u5b9e\u8df5\u4e2d\u6700\u65b9\u4fbf\uff0c\u5c31\u7528\u5b83\u4e86\uff0c\u76f4\u89c2\u4e0a\u770b\u7740\u4e5f\u633a\u5408\u7406\u3002<\/li>\n<\/ul>\n
      \u5982\u4f55\u8bad\u7ec3\uff1f\u5982\u4f55\u91c7\u6837\uff1f<\/h5>\n

      \u5f97\u5230\u4e86\u4e0a\u9762\u90a3\u4e2a\u4f18\u5316\u76ee\u6807\u4e4b\u540e\u8bad\u7ec3\u7684\u8fc7\u7a0b\u5c31\u975e\u5e38\u7b80\u6d01\u4e86\u3002<\/p>\n

      Step 1 \u53d6\u4e00\u5f20\u56fe\u7247 <\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>0<\/mn><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u6307\u5b9a\u4e00\u4e2a <\/g><\/g><\/g><\/svg>t<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u968f\u673a\u4ea7\u751f\u4e00\u4e2a <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>\u03f5<\/mi>\u223c<\/mo>N<\/mi><\/mrow>(<\/mo>0<\/mn>,<\/mo>I<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\u3002<\/p>\n

      Step 2 \u8ba1\u7b97 <\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>t<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container>\u3002<\/p>\n

      Step 3 \u628a <\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>t<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u548c <\/g><\/g><\/g><\/svg>t<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u4e22\u8fdb\u6a21\u578b\u9884\u6d4b\u4e00\u4e2a <\/g><\/g><\/g><\/g><\/g><\/svg>\u03f5<\/mi>\u03b8<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u4e0e <\/g><\/g><\/g><\/svg>\u03f5<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u6bd4\u8f83\u8ba1\u7b97 <\/g><\/g><\/g><\/g><\/g><\/svg>L<\/mi>2<\/mn><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u7136\u540e\u8ba1\u7b97\u68af\u5ea6\u66f4\u65b0\u7f51\u7edc\u3002<\/p>\n

      \u91c7\u6837\u8fc7\u7a0b\u4e5f\u987a\u6c34\u63a8\u821f\u5730\u51fa\u6765\u4e86\u3002<\/p>\n

      Step 1 \u968f\u673a\u4ea7\u751f\u4e00\u4e2a <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>T<\/mi><\/msub>\u223c<\/mo>N<\/mi><\/mrow>(<\/mo>0<\/mn>,<\/mo>I<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\u3002<\/p>\n

      Step 2 \u5bf9 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>t<\/mi>=<\/mo>T<\/mi>,<\/mo>\u22ef<\/mo>,<\/mo>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>t<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>=<\/mo>1<\/mn>\u03b1<\/mi>t<\/mi><\/msub><\/msqrt><\/mfrac>(<\/mo>x<\/mi>t<\/mi><\/msub>\u2212<\/mo>1<\/mn>\u2212<\/mo>\u03b1<\/mi>t<\/mi><\/msub><\/mrow>1<\/mn>\u2212<\/mo>\u03b1<\/mi>\u00af<\/mo><\/mover><\/mrow>t<\/mi><\/msub><\/msqrt><\/mfrac>\u03f5<\/mi>\u03b8<\/mi><\/msub>(<\/mo>x<\/mi>t<\/mi><\/msub>,<\/mo>t<\/mi>)<\/mo>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\u3002\u53ef\u4ee5\u52a0\u70b9\u968f\u673a\u6027\uff0c\u7ed9\u4e0a\u5f0f\u540e\u9762\u8865\u4e00\u4e2a <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>+<\/mo>\u03b1<\/mi>t<\/mi><\/msub>z<\/mi>,<\/mo><\/mstyle>z<\/mi>\u223c<\/mo>N<\/mi><\/mrow>(<\/mo>0<\/mn>,<\/mo>I<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\u3002<\/p>\n

      Diffusion \u7684\u5e38\u7528\u7f51\u7edc\u7ed3\u6784\u662f\u57fa\u4e8e Attention \u5c42\u548c Residual \u5757\u642d\u5efa\u7684 U-Net\uff0c\u540c\u65f6\u5f15\u5165\u5bf9\u65f6\u95f4\u6b65\u7684\u7f16\u7801\u3002<\/p>\n

      \u5b9e\u9645\u91c7\u6837\u8fc7\u7a0b\u4e2d\u53d6\u7684 <\/g><\/g><\/g><\/svg>T<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u5f80\u5f80\u8f83\u5927\uff0c\u8bba\u6587\u4e2d\u53d6 <\/g><\/g><\/g><\/g><\/g><\/svg>T<\/mi>=<\/mo>1000<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container>\u3002<\/p>\n

      <\/div>","protected":false},"excerpt":{"rendered":"

      \u554a\u2026\u2026\u53c8\u56de\u6765\u4e86\u2026\u2026\u719f\u6089\u7684 DDPM \u554a\u2026\u2026 \u8fd9\u7bc7\u6587\u7ae0\u7684\u6838\u5fc3\u8d21\u732e\u5728\u4e8e\uff1a\u63d0\u51fa\u4e00\u79cd\u57fa\u4e8e\u591a\u8f6e \u52a0\u566a \/ \u53bb\u566a \u8fdb\u884c\u56fe\u50cf […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-121","post","type-post","status-publish","format-standard","hentry","category-research"],"_links":{"self":[{"href":"https:\/\/alyname.top\/index.php\/wp-json\/wp\/v2\/posts\/121","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/alyname.top\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/alyname.top\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/alyname.top\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/alyname.top\/index.php\/wp-json\/wp\/v2\/comments?post=121"}],"version-history":[{"count":1,"href":"https:\/\/alyname.top\/index.php\/wp-json\/wp\/v2\/posts\/121\/revisions"}],"predecessor-version":[{"id":147,"href":"https:\/\/alyname.top\/index.php\/wp-json\/wp\/v2\/posts\/121\/revisions\/147"}],"wp:attachment":[{"href":"https:\/\/alyname.top\/index.php\/wp-json\/wp\/v2\/media?parent=121"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/alyname.top\/index.php\/wp-json\/wp\/v2\/categories?post=121"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/alyname.top\/index.php\/wp-json\/wp\/v2\/tags?post=121"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}