tikzcd: how to position a node in the center of two other nodes

Similar to Zarko’s solution, but with a different approach; the main trick is again using a dummy row. Specifying between origins ensures a grid like disposition.

\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz-cd}
\begin{document}

\begin{tikzcd}[column sep={6em,between origins},row sep={2.5em,between origins}]
& & & \tilde{G} \arrow[ddd,"p"] \\
& & \tilde{G} \times \tilde{G} \arrow[ru,"\tilde{m}"] & \\
\\
\tilde{G} \arrow[rruu,"1\times\tilde{I}"] \arrow[r,swap,"p"] & G
\arrow[r,swap,"1_{G}\times I"] & G \times G \arrow[r,swap,"m"] & G
\end{tikzcd}

\end{document}

A different version, with the entry between the diagonal arrows in the middle. Here the trick is to use one column more, but backing up at its sides by half the width of columns.

\documentclass{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{tikz-cd}
\begin{document}

\begin{tikzcd}[column sep={6em,between origins},row sep={2.5em,between origins},nodes in empty cells]
& &[-3em] &[-3em] & \tilde{G} \arrow[dd,"p"] \\
& & \tilde{G} \times \tilde{G} \arrow[rru,"\tilde{m}"] \\
\tilde{G} \arrow[rru,"1\times\tilde{I}"] \arrow[r,swap,"p"] &
 G \arrow[rr,swap,"1_{G}\times I"] & & G \times G \arrow[r,swap,"m"] & G
\end{tikzcd}

\end{document}

try:

\documentclass[12pt]{standalone}
\usepackage{tikz-cd}

\begin{document}
\begin{tikzcd}[nodes in empty cells,
               cells={nodes={minimum height=1.5em}}]
      & & & \tilde{G} \arrow{ddd}{p}\\
      & & \tilde{G} \times \tilde{G} \arrow{ru}{\tilde{m}} & \\%[5ex]
      & & &  \\
      \tilde{G} \arrow{rruu}{1 \times \tilde{I}} \arrow[swap]{r}{p} & G
      \arrow[swap]{r}{1_{G}\times I} & G \times G \arrow[swap]{r}{m} & G
\end{tikzcd}
\end{document}

Addendum: less steep slope is obtained by reducing the row sep and inner sep of node:

\documentclass[12pt]{standalone}
\usepackage{tikz-cd}

\begin{document}
\begin{tikzcd}[nodes in empty cells,
               row sep=-1ex, 
               cells={nodes={minimum height=1.5em, inner sep=2pt}}]
      & & & \tilde{G} \arrow{ddd}{p}\\
      & & \tilde{G} \times \tilde{G} \arrow{ru}{\tilde{m}} & \\%[5ex]
      & & &  \\
      \tilde{G} \arrow{rruu}{1 \times \tilde{I}} \arrow[swap]{r}{p} & G
      \arrow[swap]{r}{1_{G}\times I} & G \times G \arrow[swap]{r}{m} & G
\end{tikzcd}
\end{document}