The spatial and formal conception of architecture, and thus its modes of design perception and representation, directly contributes to its machine-learnability; and consequently, its capacity in leveraging today's machine learning apparatus for design innovation. If text can be sampled and synthesized in Natural Language Processing, image in Image Processing and sound in Audio Signal Processing, how can architectural forms and spaces be likewise sampled for generating new designs? The thesis endeavours to construct such a theoretical and technical framework with the concept of architectural sampling -- defined as the exemplar-learning (pedagogical), the machinic encoding (technological) and probabilistic generation (aesthetical) of architectural forms. Foundational to this technical leap is the overcoming of architecture's own longstanding set of conceptual and perceptual assumptions, namely figure/ground, parts/whole and shapes/grammars; and replaced with one that is ontologically 'flattened', 'resolutional' and 'probabilistic'. The thesis samples precursory works from the history of architecture, alongside machine learning approaches, to build its theoretical claims; while algorithmically demonstrating and technically validating them through a series of design research projects organized according to their structural characteristics (grid, sequence and hierarchy). The contribution of the work lies in its fundamental reformulation of seeing, thinking and making architectural forms through the lens of machinic sampling.