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

\def\ssep{1cm}
\def\vsep{1.5cm}
\def\yslant{0.5}
\def\xslant{-0.8}

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

\begin{scope}

\coordinate (a00) at (-2.5,-2.5);
\coordinate (a10) at (2.5,-2.5);
\coordinate (a01) at (-2.5,2.5);
\coordinate (a11) at (2.5,2.5);
\coordinate (abase) at (0,-3);
\coordinate (p1) at (-1.1,1.0);

\draw [black,fill=orange!15] plot [smooth cycle, tension=0.5] coordinates {(0,1.9) (-0.9,1.3) (-2.0,0.5) (-2.1,-0.3) (-1.4,-1.6) (0,-2.0) (1.2,-1.3) (1.4,-0.7)  (1.6,-0.3) (2.0,0.4) (0.8,1.7) };
\draw [black,fill=orange!30] plot [smooth cycle, tension=0.5] coordinates {(0,1.5) (-0.7,1.0) (-1.5,0.4) (-1.6,-0.2) (-1.0,-1.2) (0,-1.5) (0.9,-1.0) (1.1,-0.5)  (1.3,-0.2) (1.5,0.3) (0.6,1.3) };
\draw [black,fill=orange!45] plot [smooth cycle, tension=0.5] coordinates {(0,1.0) (-0.5,0.7) (-1.0,0.3) (-1.1,-0.1) (-0.7,-0.9) (0,-1.0) (0.6,-0.7) (0.8,-0.3)  (0.9,-0.1) (1.0,0.2) (0.5,0.8) };
\draw [black,fill=orange!60] plot [smooth cycle, tension=0.5] coordinates {(0,0.4) (-0.3,0.3) (-0.5,0.2) (-0.5,-0.0) (-0.4,-0.4) (0,-0.5) (0.3,-0.4) (0.5,-0.1)  (0.4,0.1) (0.2,0.4) };

\node [anchor=south] (t0label) at (0,2.8) {\small{$p_0$：$0$ 时刻的分布}};

\node [anchor=center,circle,fill=blue,minimum size=4pt,inner sep=0] (point11) at (-0.1,1.8) {};
\node [anchor=center,circle,fill=blue,minimum size=4pt,inner sep=0] (point12) at (-0.8,0.3) {};
\node [anchor=center,circle,fill=blue,minimum size=4pt,inner sep=0] (point13) at (-0.6,-0.8) {};
\node [anchor=center,circle,fill=blue,minimum size=4pt,inner sep=0] (point14) at (0.7,-1.5) {};

\end{scope}

\begin{scope}[xshift=8cm]

\coordinate (b00) at (-2.5,-2.5);
\coordinate (b10) at (2.5,-2.5);
\coordinate (b01) at (-2.5,2.5);
\coordinate (b11) at (2.5,2.5);
\coordinate (bbase) at (0,-3);
\coordinate (p2) at (-1.1,1.0);

\draw [black,fill=orange!15] plot [smooth cycle, tension=0.5] coordinates {(0,2.2) (-0.9,1.6) (-1.8,0.3) (-2.0,-0.5) (-1.2,-1.8) (0,-2.1) (0.9,-2.0) (1.7,-0.2) (1.9,0.7) (0.8,1.9) };
\draw [black,fill=orange!30] plot [smooth cycle, tension=0.5] coordinates {(0,1.6) (-0.6,1.2) (-1.4,-0.2) (-0.7,-1.2) (0,-1.5) (0.6,-1.2) (1.2,0) (1.3,0.6) (0.5,1.4)};
\draw [black,fill=orange!45] plot [smooth cycle, tension=0.5] coordinates {(0,0.8) (-0.3,0.7) (-0.8,-0.1) (-0.4,-0.7) (0,-0.8) (0.4,-0.7) (0.7,0) (0.6,0.3) (0.4,0.7)};
\draw [black,fill=orange!60] plot [smooth cycle, tension=0.5] coordinates {(0,0.4) (-0.2,0.3) (-0.4,-0.0) (-0.2,-0.3) (0,-0.4) (0.2,-0.3) (0.4,0.1) (0.2,0.3)};

\node [anchor=south] (t0label) at (0,2.8) {\small{$p_t$：$t$ 时刻的分布}};

\node [anchor=center,circle,fill=blue,minimum size=4pt,inner sep=0] (point21) at (0.2,1.7) {};
\node [anchor=center,circle,fill=blue,minimum size=4pt,inner sep=0] (point22) at (-0.1,0.1) {};
\node [anchor=center,circle,fill=blue,minimum size=4pt,inner sep=0] (point23) at (-1.3,-0.7) {};
\node [anchor=center,circle,fill=blue,minimum size=4pt,inner sep=0] (point24) at (0.1,-1.6) {};

\end{scope}

\draw [-stealth,dotted,shorten > = 1pt,shorten < = 1pt] (point11) .. controls +(60:1.3cm) and +(120:1.3cm) .. (point21);
\draw [-stealth,dotted,shorten > = 1pt,shorten < = 1pt] (point12) .. controls +(45:1.5cm) and +(110:1.5cm) .. (point22) node [pos=0.5,above,xshift=0.5cm] (sampletrajectory) {\scriptsize{由 $\Phi_{0 \to t}$ 定义的样本轨迹}};
\draw [-stealth,dotted,shorten > = 1pt,shorten < = 1pt] (point13) .. controls +(-30:1.2cm) and +(-160:1.2cm) .. (point23);
\draw [-stealth,dotted,shorten > = 1pt,shorten < = 1pt] (point14) .. controls +(-45:1.0cm) and +(-160:1.0cm) .. (point24);

\draw [->,thick,align=left] ([xshift=-0.5cm]abase) -- ([xshift=0.5cm]bbase) node [pos=0.5,below,yshift=-0.1cm] (pushforwardlabel) {\footnotesize{$\Phi_{0 \to t}$ 诱导的前推操作：$p_t = (\Phi_{0 \to t})_{\#} p_0$。}\\[-2pt] \footnotesize{分布 $p_0$ 被变换为分布 $p_t$。}};

\end{tikzpicture}
\end{document}
