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Diatom&#8722;diazotroph associations (DDAs) are symbioses where trichome-forming cyanobacteria support the host diatom with fixed nitrogen through dinitrogen (N₂) fixation. It is inferred that the growth of the trichomes is also supported by the host, but the support mechanism has not been fully quantified. Here, we develop a coarse-grained, cellular model of the symbiosis between <i>Hemiaulus</i> and <i>Richelia</i> (one of the major DDAs), which shows that carbon (C) transfer from the diatom enables a faster growth and N₂ fixation rate by the trichomes. The model predicts that the rate of N₂ fixation is 5.5 times that of the hypothetical case without nitrogen (N) transfer to the host diatom. The model estimates that 25% of fixed C from the host diatom is transferred to the symbiotic trichomes to support the high rate of N₂ fixation. In turn, 82% of N fixed by the trichomes ends up in the host. Modeled C fixation from the vegetative cells in the trichomes supports only one-third of their total C needs. Even if we ignore the C cost for N₂ fixation and for N transfer to the host, the total C cost of the trichomes is higher than the C supply by their own photosynthesis. Having more trichomes in a single host diatom decreases the demand for N₂ fixation per trichome and thus decreases their cost of C. However, even with five trichomes, which is about the highest observed for <i>Hemiaulus</i> and <i>Richelia</i> symbiosis, the model still predicts a significant C transfer from the diatom host. These results help quantitatively explain the observed high rates of growth and N₂ fixation in symbiotic trichomes relative to other aquatic diazotrophs.