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Like that

sage: p = posets.DiamondPoset(6)
sage: h = p.hasse_diagram()
sage: [h.all_paths(x,y) for x in h for y in p.principal_order_filter(x)]
[[[0]],
 [[0, 1]],
 [[0, 2]],
 [[0, 3]],
 [[0, 4]],
 [[0, 1, 5], [0, 2, 5], [0, 3, 5], [0, 4, 5]],
 [[1]],
 [[1, 5]],
 [[2]],
 [[2, 5]],
 [[3]],
 [[3, 5]],
 [[4]],
 [[4, 5]],
 [[5]]]