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update website
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felix committed Nov 11, 2024
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60 changes: 55 additions & 5 deletions index.html
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<body>
<!-- <nav class="navbar navbar-expand-md navbar-dark fixed-top bg-dark"> -->
<nav class="navbar navbar-expand-md fixed-top navbar-dark" style="background-color: #A31F34;">
<a class="navbar-brand" href="#">Steering Pre-Trained Policy with Inference-Time User Input</a>
<a class="navbar-brand" href="#">Steering Pre-Trained Diffusion Policy with Inference-Time User Input</a>

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<strong>SS</strong> is an improved version of <strong>GD</strong> that can generate trajectories closer to user input while maintaining the original motion constraints. Repeating each guided diffusion step M steps by adding back noise in a MCMC style effectively samples the correct gradients (direct adding denoising and alignment gradients in <strong>GD</strong> is in fact mathematically incorrect) of the composed distribution (original policy distribution composed with inference-time user objectives).
<strong>SS</strong> is an improved version of <strong>GD</strong> that can generate trajectories closer to user input while maintaining the original motion constraints. Repeating each guided diffusion step M steps by adding back noise in a MCMC style effectively samples the correct gradients (direct adding denoising and alignment gradients in <strong>GD</strong> is in fact <a href="https://arxiv.org/abs/2302.11552">mathematically incorrect</a>) of the composed distribution (original policy distribution composed with inference-time user objectives).
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Guided Diffusion vs. Stochastic Sampling
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Consider the toy example of composing a pre-trained policy distribution with an inference-time point input. The goal is to sample an in-distribution (highly likely) data point with respect to the pre-trained distribution while maximizing alignment with the constructed point objective distribution. <strong>GD</strong> approximately samples from the sum distribution, which can result in OOD samples that violate likelihood constraints learned by the pre-trained distribution. In contrast, <strong>SS</strong> approximately samples from the product distribution via <a href="https://arxiv.org/abs/2302.11552">Annealed MCMC</a>. See below for videos of Langevin sampling with combined denoising and alignment gradients in <strong>GD</strong> and <strong>SS</strong>.
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<img src='figs/gd_vs_ss.png' width="90%">
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<video src="figs/langevin_prior.mp4" type="video/mp4" controls="controls" class="center">
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<p style=" text-align: center;"> Unconditional sampling a pre-trained distribution</p>
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<video src="figs/langevin_gd.mp4" type="video/mp4" controls="controls" class="center">
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<p style=" text-align: center;">Conditional sampling with <strong>GD</strong></p>
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<video src="figs/langevin_ss.mp4" type="video/mp4" controls="controls" class="center">
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<p style=" text-align: center;">Conditional sampling with <strong>SS</strong></p>
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<video src="figs/exp02_dp_bi_evolution.mp4" type="video/mp4" controls="controls" class="center">
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<p style=" text-align: center;">Denoising Evolution under <strong>BI</strong></p>
<p style=" text-align: center;">Denoising evolution under <strong>BI</strong></p>
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<video src="figs/exp02_dp_gd_evolution.mp4" type="video/mp4" controls="controls" class="center">
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<p style=" text-align: center;">Denoising Evolution under <strong>GD</strong></p>
<p style=" text-align: center;">Denoising evolution under <strong>GD</strong></p>
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<video src="figs/exp02_dp_rd_evolution.mp4" type="video/mp4" controls="controls" class="center">
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<p style=" text-align: center;">Denoising Evolution under <strong>SS</strong></p>
<p style=" text-align: center;">Denoising evolution under <strong>SS</strong></p>
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