Liquid-liquid phase separation, whereby two liquids spontaneously demix, is ubiquitous in industrial, environmental, and biological processes. While isotropic fluids are known to condense into spherical droplets in the binodal region, these dynamics are poorly understood for structured fluids. Here, we report the unique observation of condensate networks, which spontaneously assemble during the demixing of a mesogen from a solvent. Condensing mesogens form rapidly elongating filaments, rather than spheres, to relieve distortion of an internal smectic mesophase. As filaments densify, they collapse into bulged discs, lowering the elastic free energy. Additional distortion is relieved by retraction of filaments into the discs, which are straightened under tension to form a ramified network. Understanding and controlling these dynamics may provide different avenues to direct pattern formation or template materials.