Previously, I set org-export-use-babel to nil, so that source code blocks in Org mode would not be evaluated, which can accelerate the export process. The results of the source code blocks were acquired via manual evaluation (press C-c C-c on code block). However, this prevents Org mode from parsing the code block header during the export. Therefore, when I use the option :exports results to export only the results without source code, it will be ignored.

This is clearly stated in the Org mode manual, Section 16.7 Exporting Code Blocks:

To stop Org from evaluating code blocks for greater security, set the ‘org-export-use-babel’ variable to ‘nil’, but understand that header arguments will have no effect.

The correct way is to keep org-export-use-babel to t and use the header argument :eval never-export to disable code block evaluation during export.

Then I can export TikZ commutative diagram as a PNG image into a markdown file without including the LaTeX source code and without running pdflatex during each export.

#+header: :headers '("\\usepackage{tikz}" "\\usepackage{tikz-cd}")
#+header: :imagemagick yes :iminoptions -density 500 :imoutoptions -trim
#+begin_src latex :exports results :eval never-export :results file raw :file figures/2025-11-19-cd-for-discretizing-op-precond.png
\begin{tikzcd}[row sep=7em, column sep=8em]
  H^{-1/2}(\Gamma)
  \arrow[r, "V"]
  \arrow[dr, red, "\mathcal{V}" swap, inner sep=2ex] &
  H^{1/2}(\Gamma)
  \arrow[r, rightharpoonup, shift left=0.5ex, "\hat{D}"]
  \arrow[d, rightharpoondown, shift right=0.5ex, "\mathcal{M}_V" left]
  \arrow[dr, rightharpoonup, red, shift left=0.5ex, "\hat{\mathcal{D}}" pos=0.3] &
  H^{-1/2}(\Gamma)
  \arrow[d, rightharpoondown, shift right=0.5ex, "\mathcal{M}_D" left]
  \arrow[l, rightharpoonup, shift left=0.5ex, "\hat{D}^{-1}"]
  \arrow[dl, rightharpoondown, shift right=0.5ex, "{[\hat{D}^{-1}]}" swap, pos=0.3] \\
  & H^{-1/2}(\Gamma)
  \arrow[u, red, rightharpoondown, shift right=0.5ex, "\mathcal{M}_V^{-1}" swap]
  \arrow[ur, blue, rightharpoondown, shift right=0.5ex, "{[\hat{D}^{-1}]^{-1}}" swap, very near start] &
  H^{1/2}(\Gamma)
  \arrow[u, red, rightharpoondown, shift right=0.5ex, "\mathcal{M}_D^{-1}" right]
  \arrow[ul, rightharpoonup, shift left=0.5ex, "\hat{\mathcal{D}}^{-1}" very near start]
\end{tikzcd}
#+end_src

#+ATTR_ORG: :width 800 :align center
#+ATTR_LATEX: :width 0.5\textwidth
#+RESULTS:
[[file:figures/2025-11-19-cd-for-discretizing-op-precond.png]]