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Abstract Foams are versatile by nature and ubiquitous in a wide range of applications, including padding, insulation, and acoustic dampening. Previous work established that foams 3D printed via Viscous Thread Printing (VTP) can in principle combine the flexibility of 3D printing with the mechanical properties of conventional foams. However, the generality of prior work is limited due to the lack of predictable process‐property relationships. In this work, a self‐driving lab is utilized that combines automated experimentation with machine learning to identify a processing subspace in which dimensionally consistent materials are produced using VTP with spatially programmable mechanical properties. In carrying out this process, an underlying self‐stabilizing characteristic of VTP layer thickness is discovered as an important feature for its extension to new materials and systems. Several complex exemplars are constructed to illustrate the newly enabled capabilities of foams produced via VTP, including 1D gradient rectangular slabs, 2D localized stiffness zones on an insole orthotic and living hinges, and programmed 3D deformation via a cable‐driven humanoid hand. Predictive mapping models are developed and validated for both thermoplastic polyurethane (TPU) and polylactic acid (PLA) filaments, suggesting the ability to train a model for any material suitable for material extrusion (ME) 3D printing.