argmax flows

**Argmax Flows** is a **generative model for discrete data that defines a continuous-time flow in a continuous latent space and maps to discrete outputs using the argmax operation** — the model generates continuous vectors and converts them to discrete tokens by taking the argmax over category dimensions. **Argmax Flow Approach** - **Continuous Latent**: Define a flow or diffusion process in a continuous latent space (one dimension per category). - **Argmax Mapping**: Map continuous vectors to discrete tokens: $x_{discrete} = ext{argmax}(z)$ over the category dimension. - **Dequantization**: Inverse direction: add continuous noise within each discrete category cell — enable continuous density estimation. - **Exact Likelihood**: Unlike discrete diffusion, argmax flows can provide exact log-likelihood bounds. **Why It Matters** - **Principled**: Provides a theoretically clean bridge between continuous generative models and discrete data. - **Density Estimation**: Enables exact likelihood computation for discrete data — useful for evaluation and comparison. - **Alternative**: Offers a different approach to discrete generation than discrete diffusion or autoregressive models. **Argmax Flows** are **continuous flows with discrete outputs** — mapping continuous generative processes to discrete tokens through the argmax operation.