Conditional Trajectories in Diffusion Models - Modeling Galaxy Evolution from Redshift
Keywords: Diffusion, Galaxy, Morphology, Redshift
Abstract: In this paper, we present a novel approach for continuous {\bf C}onditional {\bf T}rajectories on Denoising {\bf D}iffusion Probabilistic {\bf M}odels (CTDM). Focusing on physical applications, our model learns to capture the underlying relationship between galaxy images and their redshift values from training data. This enables the simulation of galaxy evolution by conditioning the reverse denoising process on future redshift values. Importantly, this is achieved without requiring multiple images of the same galaxy at different redshifts.
We demonstrate that our redshift-conditioned diffusion model learns the marginal distribution of galaxy images at each redshift value. This allows the model to generate realistic galaxy images that reflect the physical changes occurring as galaxies evolve. We derive a smoothness condition for this learned distribution, proving that the model can construct trajectories between galaxy images by incrementally changing redshift during the reverse denoising process.
Our approach offers a novel interpretation of the learned diffusion process as a means to simulate galaxy evolution, capturing both visual and physical changes over time. These techniques not only provide deeper insights into the formation and evolution of galaxies but also have broader potential applications in various areas of generative modeling.
Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)
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Submission Number: 8317
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