From 0fad3d6ee7a4cee1f5a1051ee1c665353fe93339 Mon Sep 17 00:00:00 2001 From: turnmanh <17703667+turnmanh@users.noreply.github.com> Date: Thu, 14 Dec 2023 12:45:48 -0600 Subject: [PATCH] fixed figures --- ...of-flow-matching-for-density-estimation.md | 100 +++++++++++++++--- 1 file changed, 88 insertions(+), 12 deletions(-) diff --git a/_posts/2024-05-07-elaborating-on-the-value-of-flow-matching-for-density-estimation.md b/_posts/2024-05-07-elaborating-on-the-value-of-flow-matching-for-density-estimation.md index a6f4eb62..0efdaec2 100644 --- a/_posts/2024-05-07-elaborating-on-the-value-of-flow-matching-for-density-estimation.md +++ b/_posts/2024-05-07-elaborating-on-the-value-of-flow-matching-for-density-estimation.md @@ -114,12 +114,24 @@ Moreover, the authors propose a loss function that directly regresses the time dependent vector field against the conditional vector fields with respect to single samples. -{{}} + +
+
+ {% include figure.html path="assets/img/2024-05-07-elaborating-on-the-value-of-flow-matching-for-density-estimation/imagenet.png" class="img-fluid rounded z-depth-1" %} +
+
+
+ Unconditional ImageNet-128 samples of a CNF trained using Flow Matching + with Optimal Transport probability paths. +
+ + + Assuming that the target vector field is known, the authors propose a loss function that directly regresses the time dependent vector field: @@ -179,7 +191,20 @@ $$ where $$\psi_t'$$ denotes the derivative with respect to time $$t$$. -{{ +
+ {% include figure.html path="assets/img/2024-05-07-elaborating-on-the-value-of-flow-matching-for-density-estimation/vectorfields.svg" class="img-fluid rounded z-depth-1" %} +
+ +
+ Compared to the diffusion path’s conditional score function, the OT path’s + conditional vector field has constant direction in time and is arguably + simpler to fit with a parametric model. Note the blue color denotes larger + magnitude while red color denotes smaller magnitude. +
+ + + They show that it is possible to recover certain diffusion training objectives with this choice of conditional probability paths, e.g. the variance preserving @@ -222,45 +247,96 @@ variance-preserving diffusion paths and optimal transport (OT) paths in Flow Matching. The authors explore how directly parameterizing the generating vector field and incorporating the Flow Matching objective enhances sample generation. -{{}} + +
+
+ {% include figure.html path="assets/img/2024-05-07-elaborating-on-the-value-of-flow-matching-for-density-estimation/imagegen.svg" class="img-fluid rounded z-depth-1" %} +
+
+
+ Likelihood (BPD), quality of generated samples (FID), and evaluation time + (NFE) for the same model trained with different methods. +
+ + + The findings are presented through a comprehensive evaluation using various metrics such as negative log-likelihood (NLL), Frechet Inception Distance (FID), and the number of function evaluations (NFE). Flow Matching with OT paths consistently outperforms other methods across different resolutions. -{{}} + +
+
+ {% include figure.html path="assets/img/2024-05-07-elaborating-on-the-value-of-flow-matching-for-density-estimation/sampling.svg" class="img-fluid rounded z-depth-1" %} +
+
+
+ Flow Matching, especially when using OT paths, allows us to use fewer + evaluations for sampling while retaining similar numerical error (left) and + sample quality (right). Results are shown for models trained on ImageNet + 32×32, and numerical errors are for the midpoint scheme. +
+ + + The study also delves into the efficiency aspects of Flow Matching, showcasing faster convergence during training and improved sampling efficiency, particularly with OT paths. -{{}} + +
+
+ {% include figure.html path="assets/img/2024-05-07-elaborating-on-the-value-of-flow-matching-for-density-estimation/sample_path.png" class="img-fluid rounded z-depth-1" %} +
+
+
+ Sample paths from the same initial noise with models trained on ImageNet + 64×64. The OT path reduces noise roughly linearly, while diffusion paths + visibly remove noise only towards the end of the path. Note also the + differences between the generated images. +
+ + + + + +
+
+ {% include figure.html path="assets/img/2024-05-07-elaborating-on-the-value-of-flow-matching-for-density-estimation/superres.svg" class="img-fluid rounded z-depth-1" %} +
+
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+ Image super-resolution on the ImageNet validation set. +
+ -{{}} + Additionally, conditional image generation and super-resolution experiments demonstrate the versatility of Flow Matching, achieving competitive performance