I know the smallest is 1 diamond out from my own experience in finding diamonds, and I have found 11 in one vein once. Is this the largest vein that can possibly spawn?
Minecraft generates 1 vein per chunk, but doesn't look at other chunks when doing so, so it is theoretically possible (but extremely unlikely) to find a "megavein" of 32 diamonds comprised of 4 adjacent 8-diamond veins on a chunk crossing. It's much more common to find 9-10 diamond "veins" as, say, a 4-diamond and a 6-diamond vein align along a chunk border.
Updated to version 1.18, Caves and Cliffs:
Diamond ore attempts to generate in three batches:
- The first batch generates 7 times per chunk in blobs of 0-5 ores, from Y=14 to Y=-63
- The second batch generates in 1⁄9 chunks in blobs of 0-23 ores, from Y=14 to Y=-63
- The third batch generates 4 times per chunk in blobs of 0-10 ores, from Y=14 to Y=-63
(Each one being more common as the y-level decreases.)
This means that you may eventually find a 23-diamond vein on a single chunk, with multiple 10-diamond veins on adjacent chunks. Making a grand total of 53 diamonds for a single vein. Theoretically. This seems extremely unlikely, as @Pink_killer2 suggested.