{"id":6,"date":"2025-08-15T16:47:23","date_gmt":"2025-08-15T08:47:23","guid":{"rendered":"https:\/\/alyname.top\/?p=6"},"modified":"2025-08-15T21:38:29","modified_gmt":"2025-08-15T13:38:29","slug":"flow-matching-for-generative-modeling","status":"publish","type":"post","link":"https:\/\/alyname.top\/index.php\/2025\/08\/15\/flow-matching-for-generative-modeling\/","title":{"rendered":"\u7b14\u8bb0 – Flow Matching for Generative Modeling"},"content":{"rendered":"

\u7c7b\u4f3c\u8fde\u7eed\u65f6\u95f4\u6b65\u7248\u672c\u7684 Diffusion\u3002\u6709\u4e00\u4e2a\u975e\u5e38\u4f18\u7f8e\u7684\u7ed3\u8bba\u3002<\/p>\n

\u53d1\u73b0\u6570\u5b66\u5185\u5bb9\u66f4\u591a\u7684\u8bba\u6587\u5f80\u5f80\u540d\u5b57\u66f4\u77ed<\/s><\/p>\n

[2210.02747] Flow Matching for Generative Modeling<\/a>\uff082022 \u5e74 10 \u6708\uff09<\/p>\n

\u53c2\u8003\u7684\u535a\u5ba2\uff1a\u901a\u4fd7\u6613\u61c2\u7684Flow Matching\u539f\u7406\u89e3\u8bfb\uff08\u9644\u6838\u5fc3\u516c\u5f0f\u63a8\u5bfc\u548c\u6e90\u4ee3\u7801\uff09 – \u77e5\u4e4e<\/a><\/p>\n

\u4e5f\u53c2\u8003\u4e86\u4e00\u4e0b\uff1a\u7b14\u8bb0\uff5c\u6269\u6563\u6a21\u578b\uff08\u4e00\u516b\uff09\uff1aFlow Matching \u7406\u8bba\u8be6\u89e3 | \u6975\u6771\u665d\u5be2\u611b\u597d\u5bb6<\/a><\/p>\n

\n
\u5565\u662f\u6d41\uff1f\u8981\u5e72\u5565\uff1f<\/h5>\n

\u6709\u4e00\u7ec4\u56fe\u7247\u3002\u751f\u6210\u6a21\u578b\u5e0c\u671b\u5b66\u4e60\u4e4b\u540e\u80fd\u751f\u6210\u8fd9\u4e9b\u56fe\u7247\u3002<\/p>\n

\u751f\u6210\u6a21\u578b\u7684\u4efb\u52a1\uff1a\u6709\u4e00\u4e2a\u521d\u59cb\u5206\u5e03 <\/g><\/g><\/g><\/g><\/g><\/svg>p<\/mi>0<\/mn><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container>\uff08Gaussian \u5206\u5e03\u4e4b\u7c7b\u7684\uff0c\u603b\u4e4b\u4e0d\u5305\u542b\u5f85\u751f\u6210\u56fe\u7247\u96c6\u7684\u4efb\u4f55\u4fe1\u606f\uff09\uff0c\u6709\u4e00\u4e2a\u76ee\u6807\u5206\u5e03 <\/g><\/g><\/g><\/g><\/g><\/svg>p<\/mi>1<\/mn><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container>\uff08\u5c31\u662f\u5e0c\u671b\u751f\u6210\u7684\u90a3\u4e9b\u56fe\u7247\uff09\uff0c\u5e0c\u671b\u5b66\u4e00\u4e2a\u6620\u5c04\u628a <\/g><\/g><\/g><\/g><\/g><\/svg>p<\/mi>0<\/mn><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u53d8\u6210 <\/g><\/g><\/g><\/g><\/g><\/svg>p<\/mi>1<\/mn><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container>\u3002<\/p>\n

\u4e00\u6b65\u5230\u4f4d\u7684\u751f\u6210\u4e0d\u592a\u9760\u8c31\uff1bDDPM \u7cfb\u5217\u4e2d\uff0c\u8fd9\u6837\u7684\u6620\u5c04\u662f\u5206 <\/g><\/g><\/g><\/svg>T<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u4e2a\u65f6\u95f4\u6b65\u8fdb\u884c\u7684\uff0c\u6bcf\u6b65\u662f\u4e00\u4e2a\u5c0f\u6620\u5c04\uff0c\u56e0\u6b64\u662f\u79bb\u6563\u7684\uff0c\u6211\u4eec\u8003\u8651\u5982\u679c\u628a\u8fd9\u4e2a\u8fc7\u7a0b\u53d8\u6210\u8fde\u7eed\u7684\u5462\uff1f<\/p>\n

\u73b0\u5728\u5047\u8bbe\u6211\u4eec\u5bf9\u6bcf\u4e2a <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>t<\/mi>\u2208<\/mo>[<\/mo>0<\/mn>,<\/mo>1<\/mn>]<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container> \u90fd\u6709\u4e00\u4e2a\u5206\u5e03 <\/g><\/g><\/g><\/g><\/g><\/svg>p<\/mi>t<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container>\uff1b\u53d6\u4e00\u4e2a\u521d\u59cb\u5206\u5e03\u4e2d\u7684 <\/g><\/g><\/g><\/svg>x<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5b58\u5728\u4e00\u6761\u4ee5 <\/g><\/g><\/g><\/svg>x<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u4e3a\u8d77\u70b9\u7684\u8fde\u7eed\u8def\u5f84 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>\u03c8<\/mi>t<\/mi><\/msub>(<\/mo>x<\/mi>)<\/mo>,<\/mo><\/mstyle>t<\/mi>\u2208<\/mo>[<\/mo>0<\/mn>,<\/mo>1<\/mn>]<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container> \u6700\u7ec8\u53d8\u5230\u76ee\u6807\u5206\u5e03\u91cc\u3002\u6240\u6709\u8fd9\u4e9b\u8def\u5f84\u6784\u6210\u4e00\u4e2a\u6d41\uff0c\u6211\u4eec\u8003\u8651\u5176\u901f\u5ea6\u573a <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>u<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\uff1a<\/p>\n

<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>d<\/mi>x<\/mi>=<\/mo>u<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>)<\/mo>d<\/mi>t<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

\u5047\u8bbe\u6211\u4eec\u5df2\u7ecf\u5b66\u51fa\u8fd9\u4e2a\u573a\u4e86\uff0c\u751f\u6210\u65b9\u5f0f\u5c31\u662f\u968f\u673a\u53d6\u4e00\u4e2a <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>0<\/mn><\/msub>\u223c<\/mo>p<\/mi>0<\/mn><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u7136\u540e\u6cbf <\/g><\/g><\/g><\/svg>u<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u7684\u65b9\u5411\u6d41\u52a8\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>x<\/mi>t<\/mi>+<\/mo>\u0394<\/mi>t<\/mi><\/mrow><\/msub>=<\/mo>x<\/mi>t<\/mi><\/msub>+<\/mo>u<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>t<\/mi><\/msub>)<\/mo>\u0394<\/mi>t<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

\uff08\u6216\u8005\u5b83\u7684\u8fde\u7eed\u5f62\u5f0f\uff0c\u4e3a\u4e86\u5728\u7406\u8bba\u4e0a\u8ba8\u8bba\u7684\u8bdd\uff09<\/p>\n

\u6211\u4eec\u5e0c\u671b\u6a21\u578b\u5b66\u7684\u5c31\u662f\u8fd9\u4e2a <\/g><\/g><\/g><\/svg>u<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container>\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><\/svg>L<\/mi>F<\/mi>M<\/mi><\/mrow><\/msub>=<\/mo>E<\/mi><\/mrow>t<\/mi>\u2208<\/mo>[<\/mo>0<\/mn>,<\/mo>1<\/mn>]<\/mo>,<\/mo>x<\/mi>t<\/mi><\/msub>\u223c<\/mo>p<\/mi>t<\/mi><\/msub><\/mrow><\/msub>\u2225<\/mo>u<\/mi>\u03b8<\/mi><\/msub>(<\/mo>t<\/mi>,<\/mo>x<\/mi>t<\/mi><\/msub>)<\/mo>\u2212<\/mo>u<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>t<\/mi><\/msub>)<\/mo>\u2225<\/mo>2<\/mn><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

\u4e24\u4e2a\u95ee\u9898\uff1a\u5176\u4e00\uff0c\u6211\u4eec\u6839\u672c\u4e0d\u77e5\u9053 <\/g><\/g><\/g><\/svg>u<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u662f\u5565\uff08\u5e94\u8be5\u5b58\u5728\u5f88\u591a <\/g><\/g><\/g><\/svg>u<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u4f46\u6211\u4eec\u76ee\u524d\u4e5f\u6784\u9020\u4e0d\u51fa\u4efb\u4f55\u4e00\u4e2a\u5b9e\u4f8b\uff09\uff1b\u5176\u4e8c\uff0c\u6211\u4eec\u4e0d\u77e5\u9053 <\/g><\/g><\/g><\/g><\/g><\/svg>p<\/mi>t<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u4ece\u800c\u4e5f\u6ca1\u6cd5\u53d6 <\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>t<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container>\u3002<\/p>\n

\u4f46\u662f\u6211\u4eec\u8fd8\u6839\u672c\u6ca1\u7528\u4e0a\u6211\u4eec\u7684\u56fe\u7247\u96c6 <\/g><\/g><\/g><\/g><\/g><\/svg>p<\/mi>1<\/mn><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u554a\uff01\u771f\u5b9e\u7684\u8bad\u7ec3\u8fc7\u7a0b\u80af\u5b9a\u662f\u53d6\u4e00\u5f20\u56fe\u7247 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>z<\/mi>\u223c<\/mo>p<\/mi>1<\/mn><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u7136\u540e\u5e72\u70b9\u4ec0\u4e48\u4e8b\u60c5\u2026\u2026<\/p>\n

\u8bba\u6587\u7684\u60f3\u6cd5\u662f\u8fd9\u6837\u7684\uff1a<\/p>\n

    \n
  • \u8003\u8651\u6761\u4ef6\u6d41<\/strong> <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>u<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>t<\/mi><\/msub>|<\/mo>z<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u8fd9\u4e2a\u6d41\u4f1a\u628a\u521d\u59cb\u5206\u5e03 <\/g><\/g><\/g><\/g><\/g><\/svg>p<\/mi>0<\/mn><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u53d8\u6210\u4e00\u4e2a\u5355\u70b9 <\/g><\/g><\/g><\/svg>z<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u8fd9\u6837\u7684 <\/g><\/g><\/g><\/svg>u<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u662f\u5bb9\u6613\u6784\u9020\u7684\uff1b<\/li>\n
  • \u53d1\u73b0\u7528\u6761\u4ef6\u6d41\u4f5c\u4f18\u5316\u76ee\u6807\uff0c\u4f18\u5316\u6548\u679c\u548c\u65e0\u6761\u4ef6\u6d41\u662f\u5b8c\u5168\u7b49\u4ef7<\/strong>\u7684\uff1b<\/li>\n
  • \u6784\u9020<\/strong>\u4e00\u4e2a\u5177\u4f53\u7684\u6761\u4ef6\u6d41\u3002<\/li>\n<\/ul>\n

    \u8fd9\u4e09\u4e2a\u90fd\u5b8c\u6210\u4e4b\u540e\uff0c\u8bad\u7ec3\u8fc7\u7a0b\u5c31\u53d8\u6210\u4e86\u53d6 <\/g><\/g><\/g><\/svg>z<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u7b97 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>u<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>t<\/mi><\/msub>|<\/mo>z<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u76f4\u63a5\u5b66\u3002<\/p>\n

    Step 1. <\/g><\/g><\/g><\/svg>u<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/h5>\n

    \u8fd9\u662f\u8bba\u6587\u4e2d\u7684\u5b9a\u7406 1\uff0c\u4e5f\u662f\u4e0a\u9762\u8bf4\u7684\u7b2c\u4e00\u6b65\u3002<\/p>\n

    \u5047\u8bbe\u6709 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>z<\/mi>\u223c<\/mo>q<\/mi>(<\/mo>z<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u8003\u8651\u6761\u4ef6\u5206\u5e03 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>p<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>|<\/mo>z<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container> \u548c\u8fb9\u7f18\u5206\u5e03 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>p<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container> \u4e4b\u95f4\u7684\u5173\u7cfb\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>p<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>)<\/mo>=<\/mo>\u222b<\/mo>p<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>|<\/mo>z<\/mi>)<\/mo>q<\/mi>(<\/mo>z<\/mi>)<\/mo>d<\/mi>z<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

    \n

    \u4ee5\u4e0b\u5c06 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>p<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container> \u548c <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>p<\/mi>t<\/mi><\/msub>(<\/mo>x<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container> \u6df7\u7528\u3002\u5b83\u4eec\u90fd\u8868\u793a\u65e0\u6761\u4ef6\u6d41\u3002<\/p>\n<\/blockquote>\n

    \u6ce8\u610f\u5230\u6d41\u52a8\u4e2d\u7684\u5206\u5e03 <\/g><\/g><\/g><\/g><\/g><\/svg>p<\/mi>t<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u59cb\u7ec8\u6ee1\u8db3\u5168\u6982\u7387\u4e3a <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>\u222b<\/mo>p<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>)<\/mo>d<\/mi>x<\/mi>=<\/mo>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container> \u7c7b\u4f3c\u6d41\u4f53\u7684\u8d28\u91cf\u5b88\u6052\uff1b\u6211\u4eec\u4ece\u6d41\u4f53\u529b\u5b66\u91cc\u9762\u501f\u8fc7\u6765\u4e00\u4e2a\u8fde\u7eed\u6027\u65b9\u7a0b\uff0c\u8fd9\u662f <\/g><\/g><\/g><\/g><\/g><\/svg>p<\/mi>t<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u9700\u8981\u6ee1\u8db3\u7684\u6761\u4ef6\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><\/svg>\u2202<\/mi>p<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>)<\/mo><\/mrow>\u2202<\/mi>t<\/mi><\/mrow><\/mfrac>=<\/mo>\u2212<\/mo>\u2207<\/mi>\u22c5<\/mo>(<\/mo>p<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>)<\/mo>u<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>)<\/mo>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

    \n

    \u8fde\u7eed\u6027\u65b9\u7a0b\u662f\u63cf\u8ff0\u67d0\u79cd\u7269\u7406\u91cf\u5b88\u6052\u7684\u57fa\u672c\u65b9\u7a0b\uff0c\u5e7f\u6cdb\u5e94\u7528\u4e8e\u6d41\u4f53\u529b\u5b66\u3001\u7535\u78c1\u5b66\u7b49\u9886\u57df\u3002\u5176\u6838\u5fc3\u601d\u60f3\u662f\u67d0\u4e00\u7269\u7406\u91cf\u5728\u7cfb\u7edf\u4e2d\u7684\u53d8\u5316\u7387\u7b49\u4e8e\u6d41\u5165\u548c\u6d41\u51fa\u8be5\u7cfb\u7edf\u7684\u51c0\u6d41\u91cf\u3002<\/p>\n<\/blockquote>\n

    \u73b0\u5728\u628a\u4e4b\u524d\u90a3\u4e2a\u5173\u7cfb\u5f0f\u5bf9 <\/g><\/g><\/g><\/svg>t<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u6c42\u5bfc\uff0c\u8ddf\u8fde\u7eed\u6027\u65b9\u7a0b\u5bf9\u6bd4\u4e00\u4e0b\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><\/svg>\u2202<\/mi>p<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>)<\/mo><\/mrow>\u2202<\/mi>t<\/mi><\/mrow><\/mfrac>=<\/mo>\u222b<\/mo>q<\/mi>(<\/mo>z<\/mi>)<\/mo>\u2202<\/mi>p<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>|<\/mo>z<\/mi>)<\/mo><\/mrow>\u2202<\/mi>t<\/mi><\/mrow><\/mfrac>d<\/mi>z<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

    \u6761\u4ef6\u5206\u5e03\u4e5f\u662f\u5206\u5e03\uff0c\u4ece\u800c\u4e5f\u6709\u8fde\u7eed\u6027\u65b9\u7a0b\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><\/svg>\u2202<\/mi>p<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>|<\/mo>z<\/mi>)<\/mo><\/mrow>\u2202<\/mi>t<\/mi><\/mrow><\/mfrac>=<\/mo>\u2212<\/mo>\u2207<\/mi>\u22c5<\/mo>(<\/mo>p<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>|<\/mo>z<\/mi>)<\/mo>u<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>|<\/mo>z<\/mi>)<\/mo>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

    \u73b0\u5728\u628a\u4e24\u4e2a\u8fde\u7eed\u6027\u65b9\u7a0b\u90fd\u4ee3\u8fdb\u53bb<\/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><\/svg>\u2207<\/mi>\u22c5<\/mo>(<\/mo>p<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>)<\/mo>u<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>)<\/mo>)<\/mo>=<\/mo>\u222b<\/mo>q<\/mi>(<\/mo>z<\/mi>)<\/mo>(<\/mo>\u2207<\/mi>\u22c5<\/mo>(<\/mo>p<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>|<\/mo>z<\/mi>)<\/mo>u<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>|<\/mo>z<\/mi>)<\/mo>)<\/mo>)<\/mo>d<\/mi>z<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

    \u6700\u540e\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><\/svg>u<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>)<\/mo>=<\/mo>\u222b<\/mo>q<\/mi>(<\/mo>z<\/mi>)<\/mo>p<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>|<\/mo>z<\/mi>)<\/mo>u<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>|<\/mo>z<\/mi>)<\/mo><\/mrow>p<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>)<\/mo><\/mrow><\/mfrac>d<\/mi>z<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

    \u5b8c\u5de5\uff01<\/p>\n

    \n

    \u6211\u4eec\u5728\u5e72\u4ec0\u4e48\uff1f<\/p>\n

    \u5982\u679c\u6211\u4eec\u627e\u4e86\u4e00\u4e2a\u6761\u4ef6\u6d41 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>p<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>|<\/mo>z<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\uff08\u4ece\u800c\u4e5f\u6709 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>u<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>|<\/mo>z<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\uff09\u5e76\u4e14\u77e5\u9053 <\/g><\/g><\/g><\/g><\/g><\/g><\/svg>q<\/mi>(<\/mo>z<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5219\u53ef\u4ee5\u786e\u5b9a\u65e0\u6761\u4ef6\u6d41 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>u<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\u3002\u8fd9\u4e2a\u5f0f\u5b50\u5c06\u88ab\u7528\u5728 Step 2 \u7684\u7b49\u4ef7\u6027\u8bc1\u660e\u4e2d\u3002<\/p>\n<\/blockquote>\n

    Step 2. <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>L<\/mi>C<\/mi>F<\/mi>M<\/mi><\/mrow><\/msub>=<\/mo>L<\/mi>F<\/mi>M<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/h5>\n

    \u8fd9\u662f\u8bba\u6587\u4e2d\u7684\u5b9a\u7406 2\uff0c\u4e5f\u662f\u4e0a\u9762\u8bf4\u7684\u7b2c\u4e8c\u6b65\u3002<\/p>\n

    <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>L<\/mi>F<\/mi>M<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u662f\u4ee5\u65e0\u6761\u4ef6\u6d41\u4e3a\u76ee\u6807\u7684\u4f18\u5316\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><\/svg>L<\/mi>F<\/mi>M<\/mi><\/mrow><\/msub>=<\/mo>E<\/mi><\/mrow>t<\/mi>\u2208<\/mo>[<\/mo>0<\/mn>,<\/mo>1<\/mn>]<\/mo>,<\/mo>x<\/mi>t<\/mi><\/msub>\u223c<\/mo>p<\/mi>t<\/mi><\/msub><\/mrow><\/msub>\u2225<\/mo>u<\/mi>\u03b8<\/mi><\/msub>(<\/mo>t<\/mi>,<\/mo>x<\/mi>t<\/mi><\/msub>)<\/mo>\u2212<\/mo>u<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>t<\/mi><\/msub>)<\/mo>\u2225<\/mo>2<\/mn><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

    \u53d6\u4e00\u4e2a <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>z<\/mi>\u223c<\/mo>q<\/mi>(<\/mo>z<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u4eba\u5de5\u9009\u5b9a\u4e00\u4e2a\u6761\u4ef6\u6d41 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>p<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>|<\/mo>z<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>L<\/mi>C<\/mi>F<\/mi>M<\/mi><\/mrow><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u662f\u4ee5\u6761\u4ef6\u6d41\u4e3a\u76ee\u6807\u7684\u4f18\u5316\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><\/svg>L<\/mi>C<\/mi>F<\/mi>M<\/mi><\/mrow><\/msub>=<\/mo>E<\/mi><\/mrow>t<\/mi>\u2208<\/mo>[<\/mo>0<\/mn>,<\/mo>1<\/mn>]<\/mo>,<\/mo>z<\/mi>\u223c<\/mo>q<\/mi>(<\/mo>z<\/mi>)<\/mo>,<\/mo>x<\/mi>t<\/mi><\/msub>\u223c<\/mo>p<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>|<\/mo>z<\/mi>)<\/mo><\/mrow><\/msub>\u2225<\/mo>u<\/mi>\u03b8<\/mi><\/msub>(<\/mo>t<\/mi>,<\/mo>x<\/mi>t<\/mi><\/msub>)<\/mo>\u2212<\/mo>u<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>t<\/mi><\/msub>|<\/mo>z<\/mi>)<\/mo>\u2225<\/mo>2<\/mn><\/msup><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

    \u600e\u4e48\u6837\u624d\u80fd\u8bf4\u5b83\u4eec\u7b49\u4ef7\u5462\uff1f\u6211\u4eec\u8003\u5bdf<\/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><\/svg>\u2207<\/mi>\u03b8<\/mi><\/msub>L<\/mi>C<\/mi>F<\/mi>M<\/mi><\/mrow><\/msub>=<\/mo>\u2207<\/mi>\u03b8<\/mi><\/msub>E<\/mi><\/mrow>\u2225<\/mo>u<\/mi>\u03b8<\/mi><\/msub>(<\/mo>t<\/mi>,<\/mo>x<\/mi>t<\/mi><\/msub>)<\/mo>\u2225<\/mo>2<\/mn><\/msup>\u2212<\/mo>2<\/mn>\u2207<\/mi>\u03b8<\/mi><\/msub>E<\/mi><\/mrow>[<\/mo>u<\/mi>\u03b8<\/mi><\/msub>(<\/mo>t<\/mi>,<\/mo>x<\/mi>t<\/mi><\/msub>)<\/mo>\u22c5<\/mo>u<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>t<\/mi><\/msub>|<\/mo>z<\/mi>)<\/mo>]<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

    \u548c<\/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>\u2207<\/mi>\u03b8<\/mi><\/msub>L<\/mi>F<\/mi>M<\/mi><\/mrow><\/msub>=<\/mo>\u2207<\/mi>\u03b8<\/mi><\/msub>E<\/mi><\/mrow>\u2225<\/mo>u<\/mi>\u03b8<\/mi><\/msub>(<\/mo>t<\/mi>,<\/mo>x<\/mi>t<\/mi><\/msub>)<\/mo>\u2225<\/mo>2<\/mn><\/msup>\u2212<\/mo>2<\/mn>\u2207<\/mi>\u03b8<\/mi><\/msub>E<\/mi><\/mrow>[<\/mo>u<\/mi>\u03b8<\/mi><\/msub>(<\/mo>t<\/mi>,<\/mo>x<\/mi>t<\/mi><\/msub>)<\/mo>\u22c5<\/mo>u<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>t<\/mi><\/msub>)<\/mo>]<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

    \u53ea\u8981\u5b83\u4eec\u76f8\u7b49\u5c31\u884c\u5566\uff01<\/p>\n

    \n

    \u597d\u3001\u597d\u79bb\u8c31\u7684\u64cd\u4f5c\uff0c\u4f46\u771f\u7684\u597d\u6709\u9053\u7406\u2026\u2026<\/p>\n

    \u770b\u522b\u7684\u5199\u535a\u5ba2\u7684\u4eba\u90fd\u5bf9\u6b64\u6ca1\u5565\u770b\u6cd5\uff0c\u96be\u9053\u8fd9\u662f\u4e2a\u5e38\u89c4\u64cd\u4f5c\u5417\u2026\u2026<\/s><\/p>\n<\/blockquote>\n

    \u5b83\u4eec\u76f8\u7b49\u53ea\u9700\u8981\u540e\u9762\u90a3\u9879\u76f8\u7b49\u5373\u53ef\u3002\u6211\u4eec\u5229\u7528 Step 1 \u7684\u6700\u7ec8\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><\/svg>\u2207<\/mi>\u03b8<\/mi><\/msub>E<\/mi><\/mrow>[<\/mo>u<\/mi>\u03b8<\/mi><\/msub>(<\/mo>t<\/mi>,<\/mo>x<\/mi>t<\/mi><\/msub>)<\/mo>\u22c5<\/mo>u<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>t<\/mi><\/msub>)<\/mo>]<\/mo><\/mtd>=<\/mo>\u2207<\/mi>\u03b8<\/mi><\/msub>\u222c<\/mo>u<\/mi>\u03b8<\/mi><\/msub>(<\/mo>t<\/mi>,<\/mo>x<\/mi>t<\/mi><\/msub>)<\/mo>u<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>t<\/mi><\/msub>)<\/mo>p<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>t<\/mi><\/msub>)<\/mo>d<\/mi>x<\/mi>t<\/mi><\/msub>d<\/mi>t<\/mi><\/mtd><\/mtr>=<\/mo>\u2207<\/mi>\u03b8<\/mi><\/msub>\u222c<\/mo>u<\/mi>\u03b8<\/mi><\/msub>(<\/mo>t<\/mi>,<\/mo>x<\/mi>t<\/mi><\/msub>)<\/mo>\u222b<\/mo>q<\/mi>(<\/mo>z<\/mi>)<\/mo>p<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>t<\/mi><\/msub>|<\/mo>z<\/mi>)<\/mo>u<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>t<\/mi><\/msub>|<\/mo>z<\/mi>)<\/mo><\/mrow>p<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>t<\/mi><\/msub>)<\/mo><\/mrow><\/mfrac>p<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>t<\/mi><\/msub>)<\/mo>d<\/mi>z<\/mi>d<\/mi>x<\/mi>t<\/mi><\/msub>d<\/mi>t<\/mi><\/mtd><\/mtr>=<\/mo>\u2207<\/mi>\u03b8<\/mi><\/msub>\u222d<\/mo>q<\/mi>(<\/mo>z<\/mi>)<\/mo>u<\/mi>\u03b8<\/mi><\/msub>(<\/mo>t<\/mi>,<\/mo>x<\/mi>t<\/mi><\/msub>)<\/mo>p<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>t<\/mi><\/msub>|<\/mo>z<\/mi>)<\/mo>u<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>t<\/mi><\/msub>|<\/mo>z<\/mi>)<\/mo>d<\/mi>z<\/mi>d<\/mi>x<\/mi>t<\/mi><\/msub>d<\/mi>t<\/mi><\/mtd><\/mtr>=<\/mo>\u2207<\/mi>\u03b8<\/mi><\/msub>E<\/mi><\/mrow>[<\/mo>u<\/mi>\u03b8<\/mi><\/msub>(<\/mo>t<\/mi>,<\/mo>x<\/mi>t<\/mi><\/msub>)<\/mo>\u22c5<\/mo>u<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>t<\/mi><\/msub>|<\/mo>z<\/mi>)<\/mo>]<\/mo><\/mtd><\/mtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

    \u5b8c\u5de5\uff01<\/p>\n

    \n

    \u6211\u4eec\u5728\u5e72\u4ec0\u4e48\uff1f<\/p>\n

    \u6211\u4eec\u8bc1\u660e\u4e86\uff1a\u53d6\u4e00\u4e2a <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>z<\/mi>\u223c<\/mo>q<\/mi>(<\/mo>z<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u4eba\u5de5\u9009\u5b9a\u4e00\u4e2a\u6761\u4ef6\u6d41 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>p<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>|<\/mo>z<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u4ee5 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>u<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>|<\/mo>z<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container> \u4e3a\u4f18\u5316\u76ee\u6807\u548c\u4ee5\u65e0\u6761\u4ef6 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>u<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container> \u4e3a\u4f18\u5316\u76ee\u6807\u662f\u7b49\u4ef7\u7684\u3002<\/p>\n<\/blockquote>\n

    Step 3. <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>p<\/mi>:=<\/mo>N<\/mi><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><\/h5>\n

    Gaussian \u5206\u5e03\u662f\u4e2a\u597d\u4e1c\u897f\u3002\u6211\u4eec\u5047\u8bbe <\/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>(<\/mo>t<\/mi>,<\/mo>x<\/mi>|<\/mo>z<\/mi>)<\/mo>=<\/mo>N<\/mi><\/mrow>(<\/mo>\u03bc<\/mi>t<\/mi><\/msub>,<\/mo>\u03c3<\/mi>t<\/mi>2<\/mn><\/msubsup>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\u3002<\/g><\/g><\/g><\/g><\/g><\/svg>t<\/mi>=<\/mo>0<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container> \u65f6 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>0<\/mn><\/msub>\u223c<\/mo>N<\/mi><\/mrow>(<\/mo>\u03bc<\/mi>0<\/mn><\/msub>,<\/mo>\u03c3<\/mi>0<\/mn>2<\/mn><\/msubsup>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\u3002\u6211\u4eec\u53d6\u6761\u4ef6\u6d41\u4e3a<\/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><\/svg>\u03c8<\/mi>t<\/mi><\/msub>(<\/mo>x<\/mi>0<\/mn><\/msub>|<\/mo>z<\/mi>)<\/mo>=<\/mo>\u03bc<\/mi>t<\/mi><\/msub>+<\/mo>\u03c3<\/mi>t<\/mi><\/msub>(<\/mo>x<\/mi>0<\/mn><\/msub>\u2212<\/mo>\u03bc<\/mi>0<\/mn><\/msub><\/mrow>\u03c3<\/mi>0<\/mn><\/msub><\/mfrac>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

    \n

    \u4e3a\u5565\u80fd\u8fd9\u4e48\u53d6\uff1f<\/p>\n

    \u521d\u59cb\u5206\u5e03 <\/g><\/g><\/g><\/g><\/g><\/svg>p<\/mi>0<\/mn><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u662f Gaussian \u5206\u5e03\uff0c\u6761\u4ef6\u76ee\u6807\u5206\u5e03\u662f\u5355\u70b9\uff0c\u53ef\u4ee5\u770b\u6210\u65b9\u5dee\u4e3a\u67d0\u4e2a\u5c0f\u91cf <\/g><\/g><\/g><\/g><\/g><\/svg>\u03c3<\/mi>\u03f5<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u7684 Gaussian \u5206\u5e03\uff0c\u56e0\u6b64\u4e2d\u95f4\u63d2\u4e00\u5806 <\/g><\/g><\/g><\/svg>\u03bc<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u548c <\/g><\/g><\/g><\/svg>\u03c3<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u7ebf\u6027\u53d8\u5316\u7684 Gaussian \u5206\u5e03\u662f\u8fde\u7eed\u7684\uff1b\u7136\u540e\u4e0a\u9762\u90a3\u4e2a <\/g><\/g><\/g><\/g><\/g><\/svg>\u03c8<\/mi>t<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u786e\u5b9e\u662f\u4e00\u4e2a\u6d41\u3002<\/p>\n

    \u603b\u4e4b\u80fd\u53d6\u51fa\u6765\u5c31\u884c<\/p>\n<\/blockquote>\n

    \u73b0\u5728\u6765\u7b97 <\/g><\/g><\/g><\/svg>u<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container>\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><\/g><\/g><\/g><\/g><\/g><\/svg>u<\/mi>(<\/mo>t<\/mi>,<\/mo>\u03c8<\/mi>t<\/mi><\/msub>(<\/mo>x<\/mi>0<\/mn><\/msub>)<\/mo>|<\/mo>z<\/mi>)<\/mo>=<\/mo>d<\/mi>d<\/mi>t<\/mi><\/mrow><\/mfrac>\u03c8<\/mi>t<\/mi><\/msub>(<\/mo>x<\/mi>0<\/mn><\/msub>|<\/mo>z<\/mi>)<\/mo>=<\/mo>d<\/mi>\u03bc<\/mi>t<\/mi><\/msub><\/mrow>d<\/mi>t<\/mi><\/mrow><\/mfrac>+<\/mo>x<\/mi>0<\/mn><\/msub>\u2212<\/mo>\u03bc<\/mi>0<\/mn><\/msub><\/mrow>\u03c3<\/mi>0<\/mn><\/msub><\/mfrac>d<\/mi>\u03c3<\/mi>t<\/mi><\/msub><\/mrow>d<\/mi>t<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

    \u7528 <\/g><\/g><\/g><\/svg>x<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u4ee3\u66ff <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>\u03c8<\/mi>t<\/mi><\/msub>(<\/mo>x<\/mi>0<\/mn><\/msub>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u53f3\u8fb9\u6309\u4e0a\u9762\u7684\u5b9a\u4e49\u5f0f\u6362\u5143\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><\/svg>u<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>|<\/mo>z<\/mi>)<\/mo>=<\/mo>d<\/mi>\u03bc<\/mi>t<\/mi><\/msub><\/mrow>d<\/mi>t<\/mi><\/mrow><\/mfrac>+<\/mo>x<\/mi>\u2212<\/mo>\u03bc<\/mi>t<\/mi><\/msub><\/mrow>\u03c3<\/mi>t<\/mi><\/msub><\/mfrac>d<\/mi>\u03c3<\/mi>t<\/mi><\/msub><\/mrow>d<\/mi>t<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

    \u6309\u521a\u521a\u8bf4\u7684\uff0c\u8ba9 <\/g><\/g><\/g><\/svg>\u03bc<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u548c <\/g><\/g><\/g><\/svg>\u03c3<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u7ebf\u6027\u53d8\u5316\uff0c<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>\u03bc<\/mi>t<\/mi><\/msub>=<\/mo>\u03bc<\/mi>0<\/mn><\/msub>+<\/mo>t<\/mi>(<\/mo>z<\/mi>\u2212<\/mo>\u03bc<\/mi>0<\/mn><\/msub>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>\u03c3<\/mi>t<\/mi><\/msub>=<\/mo>\u03c3<\/mi>0<\/mn><\/msub>\u2212<\/mo>t<\/mi>\u03c3<\/mi>0<\/mn><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u518d\u5047\u8bbe\u521d\u59cb\u5206\u5e03\u662f\u6807\u51c6\u6b63\u6001\u5206\u5e03\uff0c<\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/svg>\u03bc<\/mi>0<\/mn><\/msub>=<\/mo>0<\/mn>,<\/mo>\u03c3<\/mi>0<\/mn><\/msub>=<\/mo>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container>\u4ee3\u5165\uff0c\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><\/svg>u<\/mi>(<\/mo>t<\/mi>,<\/mo>x<\/mi>|<\/mo>z<\/mi>)<\/mo>=<\/mo>z<\/mi>\u2212<\/mo>(<\/mo>1<\/mn>\u2212<\/mo>\u03c3<\/mi>\u03f5<\/mi><\/msub>)<\/mo>x<\/mi><\/mrow>1<\/mn>\u2212<\/mo>(<\/mo>1<\/mn>\u2212<\/mo>\u03c3<\/mi>\u03f5<\/mi><\/msub>)<\/mo>t<\/mi><\/mrow><\/mfrac><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

    \u4e00\u4e2a\u4e0d\u9519\u7684\u76ee\u6807\u3002<\/p>\n

    \u56de\u5230 Step 2\uff0c\u6211\u4eec\u6ce8\u610f\u5230\uff0c\u8fd9\u4e2a\u8bc1\u660e\u4e2d\u7528\u5230\u7684 <\/g><\/g><\/g><\/svg>z<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container> \u5176\u5b9e\u5e76\u4e0d\u8981\u6c42\u53d6\u81ea\u76ee\u6807\u5206\u5e03 <\/g><\/g><\/g><\/g><\/g><\/svg>p<\/mi>1<\/mn><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container> \u800c\u53ef\u4ee5\u662f\u968f\u4fbf\u4ec0\u4e48\u4e1c\u897f\u3002\u73b0\u5728\u5047\u8bbe\u6211\u4eec\u5728\u521d\u59cb\u5206\u5e03\u4e2d\u968f\u673a\u91c7\u6837\u4e86\u4e00\u4e2a Gaussian \u566a\u58f0 <\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>0<\/mn><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u5728\u76ee\u6807\u5206\u5e03\u4e2d\u968f\u4fbf\u53d6\u4e86\u4e00\u4e2a\u56fe\u7247 <\/g><\/g><\/g><\/g><\/g><\/svg>x<\/mi>1<\/mn><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container>\u3002<\/p>\n

    \u4ee4 <\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/g><\/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>t<\/mi><\/msub>(<\/mo>x<\/mi>|<\/mo>x<\/mi>0<\/mn><\/msub>,<\/mo>x<\/mi>1<\/mn><\/msub>)<\/mo>=<\/mo>N<\/mi><\/mrow>(<\/mo>(<\/mo>1<\/mn>\u2212<\/mo>t<\/mi>)<\/mo>x<\/mi>0<\/mn><\/msub>+<\/mo>t<\/mi>x<\/mi>1<\/mn><\/msub>,<\/mo>\u03c3<\/mi>\u03f5<\/mi><\/msub>)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container>\uff0c\u4ee3\u5165\u4e0a\u9762\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><\/svg>u<\/mi>t<\/mi><\/msub>(<\/mo>x<\/mi>|<\/mo>x<\/mi>0<\/mn><\/msub>,<\/mo>x<\/mi>1<\/mn><\/msub>)<\/mo>=<\/mo>x<\/mi>1<\/mn><\/msub>\u2212<\/mo>x<\/mi>0<\/mn><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><\/p>\n

    wow.<\/p>\n

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

    \u7c7b\u4f3c\u8fde\u7eed\u65f6\u95f4\u6b65\u7248\u672c\u7684 Diffusion\u3002\u6709\u4e00\u4e2a\u975e\u5e38\u4f18\u7f8e\u7684\u7ed3\u8bba\u3002<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-6","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/alyname.top\/index.php\/wp-json\/wp\/v2\/posts\/6","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=6"}],"version-history":[{"count":6,"href":"https:\/\/alyname.top\/index.php\/wp-json\/wp\/v2\/posts\/6\/revisions"}],"predecessor-version":[{"id":145,"href":"https:\/\/alyname.top\/index.php\/wp-json\/wp\/v2\/posts\/6\/revisions\/145"}],"wp:attachment":[{"href":"https:\/\/alyname.top\/index.php\/wp-json\/wp\/v2\/media?parent=6"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/alyname.top\/index.php\/wp-json\/wp\/v2\/categories?post=6"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/alyname.top\/index.php\/wp-json\/wp\/v2\/tags?post=6"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}