Hi Matthew,
Thank you for contacting support. There is no direct way to view Visio drawings using Aspose.Diagram API because it does not provide any viewer control. You can convert Visio drawings to images using Aspose.Diagram API and display in the image viewer in your .NET application.
Our fellow company (GroupDocs) specializes in displaying documents within the .NET applications. GroupDocs.Viewer for .NET API can help you with this. Please refer to these helping links: GroupDocs.Viewer for .NET help topics and Download GroupDocs.Viewer for .NET
Please let us know in case of any confusion or questions.