Animals encode sensory stimuli with precisely timed activity across modalities. For example, mice can rapidly recognize odors, independent of their concentration, based on complex spatiotemporal patterns of mitral and tufted cell (MTC) activity in the olfactory bulb. Yet, it remains unknown how sequential MTC activity is organized, and what role sequential activity plays in guiding perception. Here, we performed fast 2-photon calcium imaging of hundreds of MTCs with sub-sniff temporal resolution to a battery of odors. We constructed a space of MTC tuning using the pairwise correlations between MTC odor responses averaged over a single sniff. We then analyzed the propagation of sequences in this space and discovered that sequences originated in a set of similarly tuned neurons and propagated to more distantly tuned neurons, so that the latency of MTC activation was linearly related to distance in tuning space. Further, we found that the early, but not the later part of sequences carried concentration invariant information about odor identity. Finally, inspired by the discovery that similarly tuned MTCs are activated sequentially across odors, we propose a role of activity sequences in training the piriform cortex to learn perceptually generalizable odor representations. Like the role of retinal waves in establishing the retinotopic organization of visual processing, MTCs sequentially activated together across odor responses may be responsible for establishing odor cortical maps, even for odors that have never been experienced. These ideas were tested in a proof-of-principle computational model for sequence-based unsupervised training of synapses from MTCs to the piriform cortex, which revealed that sequential activity across the entire sniff permits perceptual generalization for novel odors. The olfactory system provides a tractable model of the proposed principle that sequential activity acts as a scaffold for learning relevant activity manifolds between networks, which is applicable to other information processing circuits beyond olfaction.