Visio has an xml format (.vdx)
If you don't need Visio to help you with layout or connections, you might be able generate the xml files, then have your ASP app serve them up as consumable Visio files.
If you need Visio's Gantt-chart add-in features, or Visio's export to web or image features, then this might not be the way to go. But if you only need to place shapes on a page, set text and other data fields, and have a fairly simple layout and simple connecting lines, you should be able to go this route.
The last download link in this article is for a presentation on Visio and XML that I gave a while back:
http://www.visguy.com/2006/11/30/visio-and-xml-conference-resources/