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-              In comparing classifier-free guidance with characteristic guidance, we examine their behavior during the sampling process at time t. Classifier-free guidance applies a linear combination of positive and negative prompts at a given point along the sampling trajectory. This approach, however, does not adhere to the non-linear dynamics of the Fokker-Planck equation. On the other hand, characteristic guidance leverages the characteristic line of the Fokker-Planck equation, effectively bring the linear combination back to the initial time (t=0). At this point, the Fokker-Planck equation permits linear combinations, thereby ensuring that characteristic guidance conforms to its specifications.
+              In comparing classifier-free guidance with characteristic guidance, we examine their behavior during the sampling process at time t. Classifier-free guidance applies a linear combination of positive and negative prompts at a given point along the sampling trajectory. This approach, however, does not adhere to the non-linear dynamics of the Fokker-Planck equation. On the other hand, characteristic guidance leverages the characteristic line of the Fokker-Planck equation, effectively bring the linear combination back to the initial time (t=0). At this point, the Fokker-Planck equation permits linear combinations, thus ensuring that characteristic guidance adheres to the equation’s constraints..
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