diff --git a/after/ftplugin/markdown.vim b/after/ftplugin/markdown.vim
index 19bb301..2f8a3fa 100644
--- a/after/ftplugin/markdown.vim
+++ b/after/ftplugin/markdown.vim
@@ -1,3 +1,6 @@
+" Link completion {{{1
+set omnifunc=denote#completion#get
+
 " Go to file command |gf| adjustments {{{1
 " This resolves denote links. The function has access to the variable v:fname,
 " which corresponds to the filename under the cursor.
diff --git a/autoload/denote/completion.vim b/autoload/denote/completion.vim
new file mode 100644
index 0000000..5053784
--- /dev/null
+++ b/autoload/denote/completion.vim
@@ -0,0 +1,59 @@
+" Find the column where the completion starts. This must be between 1 and
+" col('.'). Denote links are of this form: `denote:<identifier>`.
+function s:column()
+	" Get the substring from the start of the line until col('.')
+	let l = getline(".")[:col('.')]
+	" Take the shortest prefix of a denote link. This may be any of
+	" \<d$
+	" ..
+	" \<denote:$
+	" \<denote:\f$
+	" \<denote:\f\f$
+	" etc.
+	let res = l->matchstrpos('\<denote:\f*$')
+	if res[1] >= 0
+		return res[1]
+	endif
+	let res = l->matchstrpos('\<d\f*$')
+	if res[1] == -1
+		return -3
+	endif
+	return 'denote:' =~ '^' .. res[0] ? res[1] : -3
+endfunction
+
+" Return completion items given by the base
+function s:suggestions(base)
+	let prefix = a:base->matchstr('^denote:\zs.*$')
+	let flist = glob(prefix ? "*" .. prefix .. "*" : "*", 0, v:true)
+	let res = []
+	for filename in flist
+		let noteId = denote#meta#noteIdFromFile(filename)
+		let noteTitle = denote#meta#noteTitleFromFile(filename)
+		if noteId == v:false || (noteId !~ '^' .. prefix && noteTitle !~ prefix)
+			continue
+		endif
+		let noteTitle = noteTitle ?? '(no title)'
+		let noteTags = denote#meta#noteTagsFromFile(filename)
+		let res = res->add({
+					\ 'word' : 'denote:' .. noteId,
+					\ 'abbr' : noteTitle,
+					\ 'menu' : noteTags->join(', ')
+					\ })
+	endfor
+	return res
+endfunction
+
+function! Myomni(findstart, base)
+	if a:findstart == 1
+		let tmp = s:column()
+		return tmp
+	else
+		let tmp = s:suggestions(a:base)
+		return tmp
+	endif
+endfunction
+
+" Completion function for denote links
+function denote#completion#get(findstart, base)
+	return a:findstart == 1 ? s:column() : s:suggestions(a:base)
+endfunction
diff --git a/autoload/denote/meta.vim b/autoload/denote/meta.vim
index 41eb41e..3c5b00d 100644
--- a/autoload/denote/meta.vim
+++ b/autoload/denote/meta.vim
@@ -23,10 +23,9 @@ function denote#meta#noteIdFromFile(filename)
 				\ ?? v:false
 endfunction
 
-" Return the note title from the filename. On failure, v:false is returned.
+" Return the note title from the filename.
 function denote#meta#noteTitleFromFile(filename)
 	return a:filename->matchstr("--\\zs.\\{-\\}\\ze\\(==\\|@@\\|__\\|\\..\\)")->substitute("-", " ", "g")
-				\ ?? v:false
 endfunction
 
 " Return the note tags from the filename as a list.