https://bai-yunhan.github.io/posts/Recent content in Posts on Yechao's BlogHugo -- 0.154.2en-usSun, 12 Apr 2026 00:00:00 +0000https://bai-yunhan.github.io/posts/flow-matching-section-1-the-machinery-of-generation/Sun, 12 Apr 2026 00:00:00 +0000https://bai-yunhan.github.io/posts/flow-matching-section-1-the-machinery-of-generation/A practical introduction to flow matching for generative modeling. Learn how ODEs, vector fields, and flows transport simple noise into complex data distributions, with visualizations and code.https://bai-yunhan.github.io/posts/flow-matching-section-2-constructing-training-target/Sun, 12 Apr 2026 00:00:00 +0000https://bai-yunhan.github.io/posts/flow-matching-section-2-constructing-training-target/How to construct the training target for flow matching. Covers conditional and marginal probability paths, Gaussian conditional vector fields, and the marginalization trick with proofs and visualizations.https://bai-yunhan.github.io/posts/flow-matching-section-3-constructing-training-loss/Sun, 12 Apr 2026 00:00:00 +0000https://bai-yunhan.github.io/posts/flow-matching-section-3-constructing-training-loss/Why training on the conditional vector field recovers the marginal vector field. Derives the conditional flow matching (CFM) loss, proves its equivalence to the flow matching loss, and explains the hidden-variable averaging mechanism.https://bai-yunhan.github.io/posts/vae-variational-auto-encoder/Tue, 27 Jan 2026 00:00:00 +0000https://bai-yunhan.github.io/posts/vae-variational-auto-encoder/<p>VAEs are an especially important model to study if you want to understand modern generative modeling for two reasons. First, they introduced a clean probabilistic latent-variable framework for generation—showing how to learn a distribution over hidden representations and sample from it in a principled way. Second, VAEs remain central to state-of-the-art generative systems today: in many diffusion-based models (notably latent diffusion and Stable Diffusion [1]), a VAE is the component that compresses images into a latent space and decodes generated latents back into images, making high-quality generation practical and efficient.</p>