How to generate random curves in 3D?

I would like to generate random curves in 3D. The main constraint is that the curvature of the curves should be constrained, either less than a certain maximum curvature, or by making higher curvatures less frequent using some kind of p(curvature > x) function. Aside from that, the curves can be totally random.

Bonus: I would like to generate multiple random curves in 3D such that the curves don't intersect each other or themselves, or such that they don't come closer to each other than some distance d.

The curves can be defined however, for example Bezier curves in 3D. I will eventually need to convert them to voxels (1 = curve passes through, 0 = otherwise)