Ok, dia is totally screwed up with units… here’s how to make it work well.

open dia

File -> Preferences

User Interface
  length unit: Centimeter
  Font-size unit: Point
Diagram Defaults
  Portrait
  Paper type: Letter
  Connection Points:
    Visible
    Snap to object
View Defaults
  Width: 800
  Height: 600
  Magnify: 100
  Page breaks:
    uncheck "Visible"
  Antialias:
    uncheck "view antialiased"
Grid Lines
  Visible
  Snap to
  uncheck Dynamic grid resizing
  X Size: 1.0
  Y Size: 1.0
  Lines per major line: 5

on the diagram window… File->Page Setup

Paper Size: Letter
orientation again portrait
Margins
  2.54cm all around
Scale: 100.0

View->Hide Rulers

This results in a window with 100x100pixel gridlines (when exported as png w/ or w/o alpha)

results in 5cmx5cm grids when exported directly to pdf