TikZ image of Masked Autoencoder for Distribution Estimation (MADE)

Answering my own questions, here's the completed image:

% TikZ-reproduction of fig. 1 from the paper MADE: Masked Autoencoder for Distribution Estimation (https://arxiv.org/abs/1502.03509).

documentclass[tikz]{standalone}

usepackage{xstring}

usetikzlibrary{calc,positioning}

newcommanddrawNodes[2]{
  % #1 (str): namespace
  % #2 (list[list[str]]): list of labels to print in the node of each neuron
  foreach neurons [count=lyrIdx] in #2 {
    StrCount{neurons}{,}[arrlength] % uses the xstring package
    foreach n [count=nIdx] in neurons
      node[neuron] (#1-lyrIdx-nIdx) at (arrlength/2-nIdx, 1.5*lyrIdx) {n};
  }
}

newcommanddenselyConnectNodes[2]{
  % #1 (str): namespace
  % #2 (list[int]): number of nodes in each layer
  foreach n [count=lyrIdx, remember=lyrIdx as previdx, remember=n as prevn] in #2 {
    foreach y in {1,...,n} {
      ifnum lyrIdx > 1
        foreach x in {1,...,prevn}
          draw[->] (#1-previdx-x) -- (#1-lyrIdx-y);
      fi
    }
  }
}

newcommandconnectSomeNodes[2]{
  % #1 (str): namespace
  % #2 (list[list[list[int]]]): for each node in each layer, list all connected nodes in the next layer
  foreach layer [count=lyrIdx, evaluate=lyrIdx as nextLyr using int(lyrIdx+1)] in #2
    foreach neuron [count=nIdx] in layer
        foreach edge in neuron
          draw[->] (#1-lyrIdx-nIdx) -- (#1-nextLyr-edge);
}

begin{document}
begin{tikzpicture}[
    shorten >=1pt, shorten <=1pt,
    neuron/.style={circle, draw, minimum size=4ex, thick},
    legend/.style={font=largebfseries},
  ]

  % Fully-connected neural net
  drawNodes{fcnn}{{{,,}, {,,,}, {,,,}, {,,}}}
  denselyConnectNodes{fcnn}{{3, 4, 4, 3}}

  path (fcnn-1-1) -- (fcnn-2-1) node[midway, right=1ex] (W1) {$W_1$};
  path (fcnn-2-1) -- (fcnn-3-1) node[midway, right=1ex] (W2) {$W_2$};
  path (fcnn-3-1) -- (fcnn-4-1) node[midway, right=1ex] (V) {$V$};


  % MADE net
  begin{scope}[xshift=93mm]
    drawNodes{made}{{{3,1,2}, {2,1,2,2}, {1,2,2,1}, {3,1,2}}}
    connectSomeNodes{made}{{
          {{}, {1,2,3,4}, {1,3,4}},
          {{2,3}, {1,2,3,4}, {2,3}, {2,3}},
          {{1,3}, {1}, {1}, {1,3}},
        }}
  end{scope}

  % Input + output labels
  foreach idx in {1,2,3} {
      node[below=0 of fcnn-1-idx] {$x_idx$};
      node[above=0 of fcnn-4-idx] {$hat x_idx$};
      node[below=0 of made-1-idx] {$x_idx$};
    }

  % MADE output labels
  node[xshift=2.5ex, above=0 of made-4-1] {$p(x_3|x_2)$};
  node[above=0 of made-4-2] {$p(x_2)$};
  node[xshift=-4ex, above=0 of made-4-3] {$p(x_1|x_2,x_3)$};

  % Bottom legend
  node[legend, below=of fcnn-1-2] (encoder) {autoencoder};
  node[legend, below=of made-1-2] (made) {MADE};
  node[legend, right=27mm of encoder] (masks) {masks};
  node[legend, yshift=-1pt] (masks) at ($(encoder)!0.55!(masks)$) {texttimes};
  node[legend, yshift=-1pt] (masks) at ($(masks)!0.65!(made)$) {$longrightarrow$};

  % Mask matrices
  begin{scope}[shift={(35mm,49mm)}, scale=0.4]
    draw (0,0) grid (4,3);
    node at (-1.8,1.5) {$M_V =$};
    fill[black] (0,1) rectangle ++(4,1);
    fill[black] (1,0) rectangle ++(2,1);

    begin{scope}[yshift=-5cm]
      draw (0,0) grid (4,4);
      node at (-1.8,2) {$M_{W_2} =$};
      fill[black] (0,0) rectangle ++(1,1);
      fill[black] (0,3) rectangle ++(1,1);
      fill[black] (2,0) rectangle ++(2,1);
      fill[black] (2,3) rectangle ++(2,1);
    end{scope}

    begin{scope}[yshift=-10cm]
      draw (0,0) grid (3,4);
      node at (-1.8,2) {$M_{W_1} =$};
      fill[black] (0,0) rectangle ++(1,4);
      fill[black] (2,2) rectangle ++(1,1);
    end{scope}

  end{scope}

end{tikzpicture}
end{document}

I adapted the code from Jang Soo Kim's plane partition. By creating two commands, one called mask which creates a mask line by line from bottom to top.

documentclass[]{article}
usepackage{tikz}
newcounter{x}
newcounter{y}
newcommandsquare[3]{
  fill[fill=#1, draw=black] (#2,#3) rectangle(#2+1,#3+1);
}
newcommandmask[1]{
 setcounter{y}{-1}
  foreach a in {#1} {
        addtocounter{y}{1}
        setcounter{x}{-1}
        foreach b in a {
            addtocounter{x}{1}
            ifnum b>0
            square{black}{value{x}}{value{y}}
             else   
             square{white}{value{x}}{value{y}}
             fi
    }
  }
}
begin{document}
tikzset{x={(.5,0)},y={(0,.5)}}
    begin{tikzpicture}
    begin{scope}[local bounding box=figW1]
    mask{{1,0,0},{1,0,0},{1,0,1},{1,0,0}}
    node[anchor=west,font=bf] at (figW1.east){$=M^{W^1}$};
    end{scope}

begin{scope}[yshift=3cm,local bounding box=figW2]
mask{{1,0,1,1},{0,0,0,0},{0,0,0,0},{1,0,1,1}}
node[anchor=west,font=bf] at (figW2.east){$=M^{W^2}$};
end{scope}

begin{scope}[yshift=6cm,local bounding box=figV]
mask{{0,1,1,0},{1,1,1,1},{0,0,0,0}}
node[anchor=west,font=bf] at (figV.east){$=M^{V}$};
end{scope}

    end{tikzpicture}
    

end{document}