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

where Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T = {\{ o_{i \leq n},a_{i \leq n}\}} \sim \mathcal{T}_{agent}} , Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x_{0} = {\phi{(o_{n})}}} , Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle v_{\theta^{\prime}}} is the v-prediction output of the model Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f_{\theta}} . The noise schedule Failed to parse (SVG with PNG fallback (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {\overline{\alpha}}_{t}} is linear, similarly to Rombach et al. (2022).