Copyright (c) 1995 Greg van Patten

The game can be played on any arbitrary board. We shall use the typical 8x8 board (where only orthogonal connections are valid)

LIFE and DEATH- A stone is alive, if it is adjacent to another friendly stone. Otherwise it is dead.
FIRST STAGE - Both players, in turns, drop 13 stones on some empty cells.
SECOND STAGE - On each turn, each player can do one of three things:
Relocate - Take one of his live stones, and place it on some empty cell. Is it possible that some of his own stones become dead as a consequence of relocation.
Attack - Take one of his live stones, and drop it on a cell occupied by an opponent stone (dead or alive). Then, take that stone and place it on an adjacent empty cell.
Pass - The player does nothing. However, 3 consecutive passes are not allowed.
KO RULE - A player move cannot produce a board position identical to another is some previous turn. 
GOAL - The first player who just have dead disks, looses.
An example

White has a better position, since he has more connected groups than Black. If White moves, he must attack the last three connected Black stones (h5-h6-h7), by attacking h6 (and sacrificing his own stone). E.g., d4:h6->g6. Now, Black has only two live stones, e7 and f7 and cannot avoid loosing the game on the next turn (assuming that there are no Ko position fight involved).

Some notes from the author:

If there are too many disks, the game may not end because there are not enough points for the disks to spread out. Some lattices, such as lattices with too many triangles (ie three points, each joined to the other two) make it too easy for players to keep their disks alive by continually regrouping, so that the game never ends. Here are two easily described types of lattices which seem to work well (but try others). One is any lattice where each point is connected to exactly three others. The other is a grid consisting of perpendicular families of straight lines, intersecting to form a tiling of boxes, with disks placed on the points of intersection. Even three-dimensional grids seem to work, and even higher dimensional grids might work.

For starters, try a five by five grid, and give each player five disks. A stronger player can be handicapped by giving him less disks than his opponent or by giving his opponent some extra moves in the beginning of the second stage. It is possible to think up many variations of Diffusion. For example, rank each player's disks by numbering them, and allow a disk to attack an enemy disk only if that enemy disk has the same or lower rank (you might decide that this restriction should only apply when attacking live disks, or only when attacking dead disks).

More information (including a sample game) can be found at his own diffusion page. For some related games, check Atoms and Entropy.