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<!-- Diffusion models are trained to iteratively undo a forward corruption process q that corrupts the clean data $\mathbf{x} \in \mathbb{R}^{n}$ by adding Gaussian noise. In the reverse generation process, the trained model iteratively denoises the Gaussian noise to generate clean inputs that correspond to the input data distribution. -->
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<!-- Discrete Diffusion -->
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<h4class="subtitle">Discrete Diffusion</h3>
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<p>[TODO]
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<p>[Will be completed by April 19, 2025]
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<!-- Applications of diffusion modeling to discrete data can be categorized into two broad areas. The first involves embedding discrete structures in continuous space and then performing the Gaussian diffusion defined above on these continuous representations. More related to our method are works that define a diffusion process directly on discrete structures. <a href="https://arxiv.org/abs/2107.03006">D3PM </a> introduces a framework with a Markov forward process \( q(z_t|z_{t−1}) = \text{Cat}(z_t; Q_t z_{t−1}) \), defined by the multiplication of matrices \( Q_t \in \mathbb{R}^{n \times n} \) over \( T \) discrete time steps. The matrix \( Q_t \) is designed such that \( Q_T \cdot Q_{T-1} \cdots Q_1 \mathbf{x} \) converges to a stationary distribution. -->
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