In natural settings, many stimuli impinge on our sensory organs simultaneously. Parsing these sensory stimuli into perceptual objects is a fundamental task faced by all sensory systems. Similar to other sensory modalities, increased odor backgrounds decrease the detectability of target odors by the olfactory system. The mechanisms by which background odors interfere with the detection and identification of target odors are unknown. Here we utilized the framework of the Drift Diffusion Model (DDM) to consider possible interference mechanisms in an odor detection task. We consider effects of background odors on both signal and noise in the decision-making dynamics, and show that these produce different predictions about decision accuracy and speed. To test these predictions, we trained mice to detect target odors that are embedded in random background mixtures in a two-alternative choice task. We found that the behavioral data is most consistent with background odors acting by adding noise to the decision-making dynamics. The added noise decreases the correct rate, but also decreases decision times, thereby creating a paradoxical relationship between speed and accuracy of target detection, where mice make faster and less accurate decisions in the presence of background odors.