I have this interface in the dll (this code is shown in Visual Studio from metadata):
#region Assembly XCapture.dll, v2.0.50727
// d:\\svn\\dashboard\\trunk\
So, the problem was that my DLL with IDiagnostics interface was generated from a TLB, and that TLB never got registered.
Since the DLL was imported from the TLB, RegAsm.exe refuses to register the library. So I used the regtlibv12.exe tool to register the TLB itself:
C:\Windows\Microsoft.NET\Framework\v4.0.30319\regtlibv12.exe "$(ProjectDir)\lib\Diagnostics.tlb"
Then everything magically started to work.
Since regtlibv12 is not a supported tool, I still don't know how to do this properly.