\documentclass[border=9pt]{standalone}
\input{figure_preamble.tex}
\begin{document}
\begin{tikzpicture}

\def\ssize{1}
\def\boxsize{1.3}
\def\smallsize{0.13}

\tikzstyle{snode} = [fig/module,minimum width=0.28cm,minimum height=0.28cm,inner sep=0pt]

\begin{scope}
\draw [-{Latex[scale=1.2]},thick] (0,0) -- (13.5,0);
\draw [-{Latex[scale=1.2]},thick] (0,-1.5) -- (0,2.5);
\node [anchor=north east,align=right] (ylabel) at (0-0.1,2.5) {\footnotesize{$\mathbf{x}(t)$}};
\node [anchor=north,align=left] (xlabel) at (13.3,-0.1) {\footnotesize{时间 $t$}};

\draw [Round Cap-Round Cap,blue,very thick,domain=0:12.7,samples=100] plot (\x,{0.3-0.001*(((\x-1)/1.15)^4) * (\x-1) + 0.029375*(((\x-1)/1.15)^4) + 1/(1.15)^4*(- (323/1200)*((\x-1)^3) + 0.75*((\x-1)^2))});

\node [anchor=west] (legend1) at (1.5,2.4) {\footnotesize{确定性轨迹}};
\draw [-,blue,very thick] ([xshift=-0.2cm]legend1.west) -- ([xshift=-0.8cm]legend1.west);

\node [fig/caption,anchor=north] (caption) at (6.5,-2.0) {\small{(a) ODE（确定性轨迹）}};

\end{scope}

\begin{scope}[yshift=-6.5cm]
\draw [-{Latex[scale=1.2]},thick] (0,0) -- (13.5,0);
\draw [-{Latex[scale=1.2]},thick] (0,-1.5) -- (0,2.5);
\node [anchor=north east,align=right] (ylabel) at (0-0.1,2.5) {\footnotesize{$\mathbf{x}(t)$}};
\node [anchor=north,align=left] (xlabel) at (13.3,-0.1) {\footnotesize{时间 $t$}};

\draw [Round Cap-Round Cap,blue,very thick,domain=0:12.7,samples=100] plot (\x,{(0.3-0.001*(((\x-1)/1.15)^4) * (\x-1) + 0.029375*(((\x-1)/1.15)^4) + 1/(1.15)^4*(- (323/1200)*((\x-1)^3) + 0.75*((\x-1)^2))) * ((-\x/12.7) + 1)});

\begin{pgfonlayer}{background}
\draw [Round Cap-Round Cap,name path=linetop,dotted,domain=0:12.7,samples=100] plot (\x,{(0.3-0.001*(((\x-1)/1.15)^4) * (\x-1) + 0.029375*(((\x-1)/1.15)^4) + 1/(1.15)^4*(- (323/1200)*((\x-1)^3) + 0.75*((\x-1)^2))) * ((-\x/12.7) + 1) + 1 * (\x/12.7) });
\draw [Round Cap-Round Cap,name path=linebottom,dotted,domain=0:12.7,samples=100] plot (\x,{(0.3-0.001*(((\x-1)/1.15)^4) * (\x-1) + 0.029375*(((\x-1)/1.15)^4) + 1/(1.15)^4*(- (323/1200)*((\x-1)^3) + 0.75*((\x-1)^2))) * ((-\x/12.7) + 1) - 1 * (\x/12.7) });
    \tikzfillbetween[of=linetop and linebottom,on layer=background]{orange!20}
\end{pgfonlayer}

\foreach \x in {10}{
\pgfmathsetmacro{\p}{(0.3-0.001*(((\x-1)/1.15)^4) * (\x-1) + 0.029375*(((\x-1)/1.15)^4) + 1/(1.15)^4*(- (323/1200)*((\x-1)^3) + 0.75*((\x-1)^2))) * ((-\x/12.7) + 1) + 1 * (\x/12.7) }
\pgfmathsetmacro{\q}{(0.3-0.001*(((\x-1)/1.15)^4) * (\x-1) + 0.029375*(((\x-1)/1.15)^4) + 1/(1.15)^4*(- (323/1200)*((\x-1)^3) + 0.75*((\x-1)^2))) * ((-\x/12.7) + 1) - 1 * (\x/12.7) }
\node [circle,minimum size=2pt,inner sep=0,fill=blue] (pointp) at (\x,\p) {};
\node [circle,minimum size=2pt,inner sep=0,fill=blue] (pointq) at (\x,\q) {};
\draw [<->,blue] ([yshift=-1pt]pointp.south) -- ([yshift=1pt]pointq.north);
}

\node [anchor=west] (legend1) at (1.5,2.4) {\footnotesize{确定性轨迹}};
\draw [-,blue,very thick] ([xshift=-0.2cm]legend1.west) -- ([xshift=-0.8cm]legend1.west);

\node [anchor=west] (legend2) at (1.5,1.9) {\footnotesize{随机噪声}};
\node [anchor=east,inner sep=0,draw,fill=orange!20,thin,dotted,minimum width=0.6cm,minimum height=0.2cm] (legend2label) at ([xshift=-0.2cm]legend2.west) {};

\node [anchor=south east] (noiselabel) at (10.7,0.6) {\footnotesize{噪声幅度}};

\node [fig/caption,anchor=north] (caption) at (6.5,-2.0) {\small{(b) SDE（含随机噪声）}};

\end{scope}

\end{tikzpicture}
\end{document}
figure/figure-forward-sde-example.tex

前向 SDE 将双峰非高斯分布逐渐变换为标准高斯分布。
彩色曲线表示随机轨迹，灰色曲线表示确定性的概率流 ODE 轨迹。

figure/figure-forward-sde-example.tex

说明：
1. 左侧为双峰非高斯分布 p_0(x)
2. 右侧为单峰高斯先验 p_T(x)
3. 灰色曲线表示光滑的 probability flow ODE
4. 彩色曲线表示更粗糙、更曲折的 SDE 样本轨迹

使用方式：
\begin{figure}[!t]
  \centering
  \AMLFigure{figure-forward-sde-example}
  \caption{...}
  \label{fig:forward-sde-example}
\end{figure}

