Translations:Diffusion Models Are Real-Time Game Engines/31/en: Difference between revisions

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where <math>T = {\{ o_{i \leq n},a_{i \leq n}\}} \sim \mathcal{T}_{agent}</math>, <math>x_{0} = {\phi{(o_{n})}}</math>, <math>t \sim {\mathcal{U}{(0,1)}}</math>, <math>\epsilon \sim {\mathcal{N}{(0,\mathbf{I})}}</math>, <math>x_{t} = {{\sqrt{{\overline{\alpha}}_{t}}x_{0}} + {\sqrt{1 - {\overline{\alpha}}_{t}}\epsilon}}</math>, <math>{v{(\epsilon,x_{0},t)}} = {{\sqrt{{\overline{\alpha}}_{t}}\epsilon} - {\sqrt{1 - {\overline{\alpha}}_{t}}x_{0}}}</math>, and <math>v_{\theta^{\prime}}</math> is the v-prediction output of the model <math>f_{\theta}</math>. The noise schedule <math>{\overline{\alpha}}_{t}</math> is linear, similarly to Rombach et al. ([https://arxiv.org/html/2408.14837v1#bib.bib26 2022]).

where $T={\{o_{i\leq n},a_{i\leq n}\}}\sim {\mathcal {T}}_{agent}$ , $x_{0}={\phi {(o_{n})}}$ , $t\sim {{\mathcal {U}}{(0,1)}}$ , $\epsilon \sim {{\mathcal {N}}{(0,\mathbf {I} )}}$ , $x_{t}={{{\sqrt {{\overline {\alpha }}_{t}}}x_{0}}+{{\sqrt {1-{\overline {\alpha }}_{t}}}\epsilon }}$ , ${v{(\epsilon ,x_{0},t)}}={{{\sqrt {{\overline {\alpha }}_{t}}}\epsilon }-{{\sqrt {1-{\overline {\alpha }}_{t}}}x_{0}}}$ , and $v_{\theta ^{\prime }}$ is the v-prediction output of the model $f_{\theta }$ . The noise schedule ${\overline {\alpha }}_{t}$ is linear, similarly to Rombach et al. (2022).