The SVD fires a different round, 7.62x54mmR, from the AK/AKM's 7.62x39mm. A 7.62x54mmR automatic rifle wouldn't qualify as an assault rifle, as that's a full-size round, making it a battle rifle, which wasn't ever really something the Soviet (or Chinese, for that matter) bloc embraced. (While the USSR did use the SVT-38/40, this is more equivalent to late '30s/'40s-era semi-automatic rifles like the Garand, MAS-49, and SAFN-49 than "true" battle rifles like the prototypical FAL, G3, and M14.)
For an actual assault rifle - in Soviet terms, effectively either 7.62 or 5.45x39mm - there really wouldn't have ever been a need to derive one from the SVD. Short-stroke gas piston operation (the most fundamental difference between the AK and SVD) is hardly unique to the SVD. An AK-pattern rifle using that system would use the same operating principle as the SVD, but it would've been designed around the principle (short-stroke operation), rather than around a rifle (SVD) that used that principle, which is a rather pointlessly roundabout way of doing things. (Some AK-pattern assault rifles like the Zastava M21 and aforementioned Type 81/QBZ-81 actually use short-stroke piston operation, but they're certainly no SVD variants.)
