Are there conventional processes by which one can construct a material that gradually transitions from one alloy or molecular density to another? For instance if I wanted a material that gradually transitioned from steel to cast iron or from rubber with one molecular density to another, I'm sure it's different for different material, but is there at least a name for that type of process?
There are a couple of processes I can think of that involve gradual changes in chemical composition. Carburization, or the diffusion of carbon into steel, is very common. The end result is a hard, high-carbon surface that gradually gives way to a generally softer, relatively low-carbon core. Similar surface diffusion processes are used for many materials. Even most 'plating' processes usually have a very thin layer of inter-diffusion.
Some ceramic processing techniques involving colloidal suspensions can result in larger particles settling toward the bottom of the gel, producing a density gradient in the finished product. This is usually a bad thing, though.
As the first answer implied, chemical gradients in materials are usually the result of interrupted diffusion. I have heard of additive manufacturing techniques that involve layer-by-layer, gradual alterations in the chemical composition of a metal--but my understanding is that these are mostly experimental at the moment.
There is a process that might do something similar to what you aim for, it is called “diffusion bonding”. However, this process is feasible only for materials that do diffuse (in the chemical sense) into each other. It is not a common process because it needs a long long time, warming up the two things to bond may enhance it a bit but still very slow. Usually you would use such process to bond two different metals that can’t be welded otherwise