Diagenesis refers to any physical and/or chemical effects that occur after burial of plant and animal matter. The most common physical change is flattening by the weight of sediment deposited above the buried specimen. Flattening can occur very soon after burial or may take millions of years. The most common diagenetic process is the conversion of aragonite to calcite.
Reference sited: Michael J. Benton, and David A.T. Harper. Introduction to Paleobiology and the Fossil Record. 2009
Diagenesis as defined in relation to geology: "sum of all processes, chiefly chemical, by which changes in a sediment are brought about after its deposition but before its final lithification (conversion to rock)...An example of diagenesis is the chemical alteration of a feldspar to form a distinctly new mineral in its place, a clay mineral." http://www.britannica.com/EBchecked/topic/161033/diagenesis
Whether we are dealing with organic or inorganic material, definitions seem very similar. Effects on the original material after burial leading up to and including lithification.