Blue diamonds are chinchillas that have both the sapphire and violet gene expressed. Both genes are recessive genes, so to get a blue diamond, you need parents that carry both genes. These could be a variety of different chinchillas, but regardless of which they are... each parent would need to be one of these:
sapphire, violet carrier
violet, sapphire carrer
standard grey, sapphire & violet carrier
This way, both the parents would have both the sapphire and violet genes to pass down to their offspring.
However, just because they can pass along these genes, does not mean that they do. Short of breeding a blue diamond to a blue diamond (which is not a good idea, genetically -- you will end up with weak furred, not good quality animals), you will never end up with 100% blue diamonds.
For example, let's say you breed a sapphire, violet carrier (mom) to a violet, sapphire carrier (dad). In mom, the sapphire is actually expressed, so all babies will have to be sapphire carriers. As for the violet that she is carrying, a carried gene will only produce babies that carry that gene, 50% of the time. So just from her side, the babies look like this:
standard, sapphire carrier, violet carrier
standard, sapphire carrier
Now... as the carried genes are not expressed... it's anyone's guess as far as WHICH of those standards would be the ones carrying both sapphire and violet. The only way would be to breed them down the line.
But hold on, we have dad's genetics too. As dad is a violet, sapphire carrier, this means that his babies would look like this:
standard, violet carrier, sapphire carrier
standard, violet carrier
Of course, that's only one half of the puzzle, so when you put these chinchillas together, what you end up is this:
--blue diamonds (1/4 of babies -- as the chins that receive both sapphire & violet carrier genes from both parents will be blue diamonds)
--violet, sapphire carriers (1/4 of babies), as the chins that receive both sapphire & violet carrier genes from one parent, and violet carrier genes from the other parent will express the violet gene, but will only carry the sapphire
--sapphire, violet carriers (1/4 of babies), as the chins that receive both sapphire & violet genes from one parent, and sapphire carrier genes from the other parent, they will express the sapphire gene, but only carry the violet
--standard grey, sapphire & violet carrier (1/4 of babies), as some babies will receive only a sapphire gene from one parent and only a violet gene from the other
Now, this is all fine and dandy, but in reality... it may not be one in four babies that's really blue diamond. Just as an example, I had a female litter the other day. She is a standard grey, bred to a pink white male, which should produce 25% standard grey, 25% hetero beige, 25% mosaic, and 25% pink white. She actually had four babies, so this works great for this example... she had three standard greys and one hetero beige. Which, in the blue diamond example, would be like having three standard grey, sapphire & violet carriers, and a sapphire, violet carrier. That's why blue diamonds are not cheap.
Color-wise, these colors are different. Violets are more of a purplish-tinged grey, sort of like a dove grey. Sapphires are more of a blue-grey, sort of like a light light grey. Blue diamonds are almost a powdery blue color.
This is a violet:
This is a sapphire wrap (darker than usual sapphire because of the ebony gene that creates the wrap, but you can see the blue vs. purplish):
And this is a blue diamond:
Of course, they look different in person, and under perfect lighting... but often people say that it's hard for them to tell the difference in pictures. Some of that does depend on monitor settings and how the photo looks in general, but to try to help, we took a pic of some side by side.
While these are not the greatest pictures ever, the blue diamond is on the left, and the violet is on the right. Whether you knew which colors those were, most people can say that they can tell that the grey coloration on the two chins does have a different tone to it, and that's the difference in color.