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---
# Feel free to add content and custom Front Matter to this file.
# To modify the layout, see https://jekyllrb.com/docs/themes/#overriding-theme-defaults
layout: default
---
<style>
.video-container {
position: relative;
padding-bottom: 56.25%; /* 16:9 aspect ratio */
height: 0;
overflow: hidden;
max-width: 100%;
background: #000;
}
.video-container iframe {
position: absolute;
top: 0;
left: 0;
width: 100%;
height: 100%;
}
audio {
width: 100%;
}
table {
width: 100%;
border-collapse: collapse;
}
.table-container {
width: 100%;
max-width: 100%;
overflow-x: auto;
-webkit-overflow-scrolling: touch; /* For smooth scrolling on mobile devices */
}
html, body {
margin: 5px; /* Get rid of default margins */
padding: 5px; /* Get rid of default padding */
overflow-x: hidden; /* Prevent horizontal overflow */
}
th, td {
padding: 4px;
text-align: left;
border: 1px solid #ddd;
font-size: 1em; /* Base font size */
white-space: nowrap;
}
p {
text-align: justify;
hyphens: auto;
}
div {
margin: 0;
padding: 0;
box-sizing: border-box;
max-width: 100%;
}
/* Define a class for left-aligned text */
.left-align {
text-align: left;
hyphens: none;
}
.container {
max-width: 100%;
background-color: #f4f4f4;
align-items: left;
overflow-x: auto; /* Handle overflow */
padding: 0;
margin: 0 auto;
position: relative;
}
.inner-container {
width: calc(100% - 30px);
background-color: #f4f4f4;
align-items: left;
padding: 0;
margin: 0 auto;
overflow: hidden;
position: relative; /* Relative positioning for absolute child positioning */
}
pre {
width: calc(100% - 30px);
background-color: #f4f4f4;
border: 0;
padding: 0px;
overflow: auto;
border-radius: 0px;
margin: 0;
}
code {
font-family: monospace;
padding: 0px;
margin: 0;
}
.highlight {
cursor: pointer;
padding: 4px 4px;
background-color: #f4f4f4;
border: 0;
color: white;
border-radius: 4px;
display: flex;
align-items: center;
max-width: 100%;
position: absolute;
top: 0; /* Position the button at the top */
right: 0; /* Position the button at the right edge */
margin: 5px; /* Small margin for aesthetics */
}
.highlight svg {
fill: #4e4e4e;
margin-right: 5px;
}
.highlight:hover {
background-color: #d3d3d3;
}
</style>
<h1 style="font-size: 1.8em;">
Investigating Training Objectives for Generative Speech Enhancement
</h1>
<p class="left-align"></p>
Julius Richter, Danilo de Oliveira, Timo Gerkmann
</p>
<p>
Generative speech enhancement has recently shown promising advancements in improving speech quality in noisy
environments. Multiple diffusion-based frameworks exist, each employing distinct training objectives and learning
techniques. This paper aims at explaining the differences between these frameworks by focusing our investigation on
score-based generative models and Schrödinger bridge. We conduct a series of comprehensive experiments to compare
their performance and highlight differing training behaviors. Furthermore, we propose a novel perceptual loss
function tailored for the Schrödinger bridge framework, demonstrating enhanced performance and improved perceptual
quality of the enhanced speech signals. All experimental code and pre-trained models are publicly available to
facilitate further research and development in this domain.
</p>
<h2>
Results on VB-DMD (matched)
</h2>
<p>
We evaluate the performance of the proposed models on the VoiceBank-Demand (VB-DMD) dataset. The results are
summarized in the table below. Models M1-M4 are based on score-based generative models for speech enhancement
(SGMSE) <span class="reference" data-ref="sgmse"></span>, while M5-M8 are based on the Schrödinger bridge framework
<span class="reference" data-ref="sbse"></span>.
</p>
<div class="table-container">
<table style="width:100%; border-collapse: collapse;">
<caption style="caption-side: bottom; text-align: left; padding: 8px; font-style: italic;">
<strong>Table: Speech Enhancement Performance on VB-DMD.</strong> Values indicate the mean of the metrics.
</caption>
<thead>
<tr style="border-top: 2px solid black; border-bottom: 2px solid black;">
<th>Model</th>
<th style="text-align: right;">POLQA</th>
<th style="text-align: right;">PESQ</th>
<th style="text-align: right;">SI-SDR</th>
<th style="text-align: right;">ESTOI</th>
<th style="text-align: right;">DNSMOS</th>
</tr>
</thead>
<tbody>
<tr style="border-bottom: 2px solid black;">
<td>Noisy</td>
<td style="text-align: right;">3.11</td>
<td style="text-align: right;">1.97</td>
<td style="text-align: right;">8.4</td>
<td style="text-align: right;">0.79</td>
<td style="text-align: right;">3.09</td>
</tr>
<tr>
<td>Conv-TasNet <span class="reference" data-ref="convtasnet"></span></td>
<td style="text-align: right;">3.56</td>
<td style="text-align: right;">2.63</td>
<td style="text-align: right;">19.1</td>
<td style="text-align: right;">0.85</td>
<td style="text-align: right;">3.37</td>
</tr>
<tr>
<td>MetricGAN+ <span class="reference" data-ref="metricgan"></span></td>
<td style="text-align: right;">3.72</td>
<td style="text-align: right;">3.13</td>
<td style="text-align: right;">8.5</td>
<td style="text-align: right;">0.83</td>
<td style="text-align: right;">3.37</td>
</tr>
<tr>
<td>SE-MAMBA <span class="reference" data-ref="se-mamba"></span></td>
<td style="text-align: right;"><strong>4.33</strong></td>
<td style="text-align: right;">3.56</td>
<td style="text-align: right;"><strong>19.7</strong></td>
<td style="text-align: right;"><strong>0.89</strong></td>
<td style="text-align: right;">3.58</td>
</tr>
<tr style="border-bottom: 2px solid black;">
<td>SGMSE+ <span class="reference" data-ref="sgmse"></span></td>
<td style="text-align: right;">3.95</td>
<td style="text-align: right;">2.93</td>
<td style="text-align: right;">17.3</td>
<td style="text-align: right;">0.87</td>
<td style="text-align: right;">3.56</td>
</tr>
<tr>
<td>M1</td>
<td style="text-align: right;">3.93</td>
<td style="text-align: right;">2.84</td>
<td style="text-align: right;">17.7</td>
<td style="text-align: right;">0.86</td>
<td style="text-align: right;">3.54</td>
</tr>
<tr>
<td>M2</td>
<td style="text-align: right;">3.96</td>
<td style="text-align: right;">2.90</td>
<td style="text-align: right;">18.0</td>
<td style="text-align: right;">0.86</td>
<td style="text-align: right;">3.55</td>
</tr>
<tr></tr>
<td>M3</td>
<td style="text-align: right;">3.86</td>
<td style="text-align: right;">2.77</td>
<td style="text-align: right;">17.8</td>
<td style="text-align: right;">0.86</td>
<td style="text-align: right;">3.51</td>
</tr>
<tr>
<td>M4 (EDM2)</td>
<td style="text-align: right;">3.87</td>
<td style="text-align: right;">2.87</td>
<td style="text-align: right;">18.0</td>
<td style="text-align: right;">0.86</td>
<td style="text-align: right;">3.54</td>
</tr>
<tr>
<td>M5</td>
<td style="text-align: right;">4.15</td>
<td style="text-align: right;">2.91</td>
<td style="text-align: right;">19.4</td>
<td style="text-align: right;">0.88</td>
<td style="text-align: right;"><strong>3.59</strong></td>
</tr>
<tr>
<td>M6</td>
<td style="text-align: right;">4.15</td>
<td style="text-align: right;"><strong>3.70</strong></td>
<td style="text-align: right;">8.3</td>
<td style="text-align: right;">0.86</td>
<td style="text-align: right;">3.44</td>
</tr>
<tr>
<td>M7</td>
<td style="text-align: right;">4.25</td>
<td style="text-align: right;">3.50</td>
<td style="text-align: right;">14.1</td>
<td style="text-align: right;">0.87</td>
<td style="text-align: right;">3.55</td>
</tr>
<tr style="border-bottom: 2px solid black;">
<td>M8</td>
<td style="text-align: right;">4.20</td>
<td style="text-align: right;">3.44</td>
<td style="text-align: right;">15.3</td>
<td style="text-align: right;">0.87</td>
<td style="text-align: right;">3.58</td>
</tr>
</tbody>
</table>
</div>
<h2>
Audio Examples
</h2>
<p>Select an audio file:
<select id="audioSelect" onchange="playAudio()">
<option value="p257_258">p257_258</option>
<option value="p232_198">p232_198</option>
<option value="p257_066">p257_066</option>
<option value="p232_067">p232_067</option>
<option value="p257_419">p257_419</option>
<option value="p232_017">p232_017</option>
<option value="p257_411">p257_411</option>
<option value="p232_189">p232_189</option>
<option value="p257_403">p257_403</option>
<option value="p232_394">p232_394</option>
<option value="p257_410">p257_410</option>
<option value="p232_035">p232_035</option>
<option value="p257_354">p257_354</option>
<option value="p232_160">p232_160</option>
<option value="p257_343">p257_343</option>
<option value="p232_409">p232_409</option>
<option value="p257_077">p257_077</option>
<option value="p232_023">p232_023</option>
<option value="p257_350">p257_350</option>
<option value="p232_107">p232_107</option>
</select>
</p>
<p>
Noisy: <br>
<audio id="audioPlayerNoisy" controls>
<source id="audioSourceNoisy" src="https://www2.informatik.uni-hamburg.de/sp/audio/publications/icassp2025_gense/noisy/p257_258.wav" type="audio/wav">
Your browser does not support the audio element.
</audio><br>
Clean: <br>
<audio id="audioPlayerClean" controls>
<source id="audioSourceClean" src="https://www2.informatik.uni-hamburg.de/sp/audio/publications/icassp2025_gense/clean/p257_258.wav" type="audio/wav">
Your browser does not support the audio element.
</audio><br>
Conv-TasNet <span class="reference" data-ref="convtasnet"></span>:<br>
<audio id="audioPlayerConvTasNet" controls>
<source id="audioSourceConvTasNet" src="https://www2.informatik.uni-hamburg.de/sp/audio/publications/icassp2025_gense/convtasnet/p257_258.wav" type="audio/wav">
Your browser does not support the audio element.
</audio><br>
MetricGAN+ <span class="reference" data-ref="metricgan"></span>:<br>
<audio id="audioPlayerMetricGAN" controls>
<source id="audioSourceMetricGAN" src="https://www2.informatik.uni-hamburg.de/sp/audio/publications/icassp2025_gense/metricgan/p257_258.wav" type="audio/wav">
Your browser does not support the audio element.
</audio><br>
SE-MAMBA <span class="reference" data-ref="se-mamba"></span>:<br>
<audio id="audioPlayerSEMAMBA" controls>
<source id="audioSourceSEMAMBA" src="https://www2.informatik.uni-hamburg.de/sp/audio/publications/icassp2025_gense/se_mamba/p257_258.wav" type="audio/wav">
Your browser does not support the audio element.
</audio><br>
SGMSE+ <span class="reference" data-ref="sgmse"></span>:<br>
<audio id="audioPlayerSGMSE" controls>
<source id="audioSourceSGMSE" src="https://www2.informatik.uni-hamburg.de/sp/audio/publications/icassp2025_gense/sgmse/p257_258.wav" type="audio/wav">
Your browser does not support the audio element.
</audio><br>
M1:<br>
<audio id="audioPlayerM1" controls>
<source id="audioSourceM1" src="https://www2.informatik.uni-hamburg.de/sp/audio/publications/icassp2025_gense/m1/p257_258.wav" type="audio/wav">
Your browser does not support the audio element.
</audio><br>
M2:<br>
<audio id="audioPlayerM2" controls>
<source id="audioSourceM2" src="https://www2.informatik.uni-hamburg.de/sp/audio/publications/icassp2025_gense/m2/p257_258.wav" type="audio/wav">
Your browser does not support the audio element.
</audio><br>
M3:<br>
<audio id="audioPlayerM3" controls>
<source id="audioSourceM3" src="https://www2.informatik.uni-hamburg.de/sp/audio/publications/icassp2025_gense/m3/p257_258.wav" type="audio/wav">
Your browser does not support the audio element.
</audio><br>
M4 (EDM2):<br>
<audio id="audioPlayerM4" controls>
<source id="audioSourceM4" src="https://www2.informatik.uni-hamburg.de/sp/audio/publications/icassp2025_gense/m4/p257_258.wav" type="audio/wav">
Your browser does not support the audio element.
</audio><br>
M5:<br>
<audio id="audioPlayerM5" controls>
<source id="audioSourceM5" src="https://www2.informatik.uni-hamburg.de/sp/audio/publications/icassp2025_gense/m5/p257_258.wav" type="audio/wav">
Your browser does not support the audio element.
</audio><br>
M6:<br>
<audio id="audioPlayerM6" controls>
<source id="audioSourceM6" src="https://www2.informatik.uni-hamburg.de/sp/audio/publications/icassp2025_gense/m6/p257_258.wav" type="audio/wav">
Your browser does not support the audio element.
</audio><br>
M7:<br>
<audio id="audioPlayerM7" controls>
<source id="audioSourceM7" src="https://www2.informatik.uni-hamburg.de/sp/audio/publications/icassp2025_gense/m7/p257_258.wav" type="audio/wav">
Your browser does not support the audio element.
</audio><br>
M8:<br>
<audio id="audioPlayerM8" controls>
<source id="audioSourceM8" src="https://www2.informatik.uni-hamburg.de/sp/audio/publications/icassp2025_gense/m8/p257_258.wav" type="audio/wav">
Your browser does not support the audio element.
</audio>
</p>
<script>
function playAudio() {
var audioPlayerNoisy = document.getElementById('audioPlayerNoisy');
var audioPlayerClean = document.getElementById('audioPlayerClean');
var audioPlayerConvTasNet = document.getElementById('audioPlayerConvTasNet');
var audioPlayerMetricGAN = document.getElementById('audioPlayerMetricGAN');
var audioPlayerSEMAMBA = document.getElementById('audioPlayerSEMAMBA');
var audioPlayerSGMSE = document.getElementById('audioPlayerSGMSE');
var audioPlayerM1 = document.getElementById('audioPlayerM1');
var audioPlayerM2 = document.getElementById('audioPlayerM2');
var audioPlayerM3 = document.getElementById('audioPlayerM3');
var audioPlayerM4 = document.getElementById('audioPlayerM4');
var audioPlayerM5 = document.getElementById('audioPlayerM5');
var audioPlayerM6 = document.getElementById('audioPlayerM6');
var audioPlayerM7 = document.getElementById('audioPlayerM7');
var audioPlayerM8 = document.getElementById('audioPlayerM8');
var audioSourceNoisy = document.getElementById('audioSourceNoisy');
var audioSourceClean = document.getElementById('audioSourceClean');
var audioSourceConvTasNet = document.getElementById('audioSourceConvTasNet');
var audioSourceMetricGAN = document.getElementById('audioSourceMetricGAN');
var audioSourceSEMAMBA = document.getElementById('audioSourceSEMAMBA');
var audioSourceSGMSE = document.getElementById('audioSourceSGMSE');
var audioSourceM1 = document.getElementById('audioSourceM1');
var audioSourceM2 = document.getElementById('audioSourceM2');
var audioSourceM3 = document.getElementById('audioSourceM3');
var audioSourceM4 = document.getElementById('audioSourceM4');
var audioSourceM5 = document.getElementById('audioSourceM5');
var audioSourceM6 = document.getElementById('audioSourceM6');
var audioSourceM7 = document.getElementById('audioSourceM7');
var audioSourceM8 = document.getElementById('audioSourceM8');
var selectedAudio = document.getElementById('audioSelect').value;
if (selectedAudio) {
// Set the source of the source elements, not the audio players
audioSourceNoisy.src = "https://www2.informatik.uni-hamburg.de/sp/audio/publications/icassp2025_gense/noisy/" + selectedAudio + ".wav";
audioPlayerNoisy.load(); // Load the selected audio file using the audio player
audioSourceClean.src = "https://www2.informatik.uni-hamburg.de/sp/audio/publications/icassp2025_gense/clean/" + selectedAudio + ".wav";
audioPlayerClean.load(); // Load the selected audio file using the audio player
audioSourceConvTasNet.src = "https://www2.informatik.uni-hamburg.de/sp/audio/publications/icassp2025_gense/convtasnet/" + selectedAudio + ".wav";
audioPlayerConvTasNet.load(); // Load the selected audio file using the audio player
audioSourceMetricGAN.src = "https://www2.informatik.uni-hamburg.de/sp/audio/publications/icassp2025_gense/metricgan/" + selectedAudio + ".wav";
audioPlayerMetricGAN.load(); // Load the selected audio file using the audio player
audioSourceSEMAMBA.src = "https://www2.informatik.uni-hamburg.de/sp/audio/publications/icassp2025_gense/se_mamba/" + selectedAudio + ".wav";
audioPlayerSEMAMBA.load(); // Load the selected audio file using the audio player
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<br>
<h2>
Results on EARS-WHAM (mismatched)
</h2>
<div class="table-container">
<table style="width:100%; border-collapse: collapse;">
<caption style="caption-side: bottom; text-align: left; padding: 8px; font-style: italic;">
<strong>Table: Speech Enhancement Performance on EARS-WHAM.</strong> Values indicate the mean of the metrics.
</caption>
<thead>
<tr style="border-top: 2px solid black; border-bottom: 2px solid black;">
<th>Model</th>
<th style="text-align: right;">POLQA</th>
<th style="text-align: right;">PESQ</th>
<th style="text-align: right;">SI-SDR</th>
<th style="text-align: right;">ESTOI</th>
<th style="text-align: right;">DNSMOS</th>
</tr>
</thead>
<tbody>
<tr style="border-bottom: 2px solid black;">
<td>Noisy</td>
<td style="text-align: right;">1.82</td>
<td style="text-align: right;">1.25</td>
<td style="text-align: right;">6.0</td>
<td style="text-align: right;">0.49</td>
<td style="text-align: right;">2.74</td>
</tr>
<tr>
<td>M1</td>
<td style="text-align: right;">2.35</td>
<td style="text-align: right;">1.85</td>
<td style="text-align: right;">6.8</td>
<td style="text-align: right;">0.60</td>
<td style="text-align: right;">3.67</td>
</tr>
<tr>
<td>M2</td>
<td style="text-align: right;">2.49</td>
<td style="text-align: right;">1.90</td>
<td style="text-align: right;">6.8</td>
<td style="text-align: right;">0.61</td>
<td style="text-align: right;">3.74</td>
</tr>
<tr>
<td>M3</td>
<td style="text-align: right;">1.12</td>
<td style="text-align: right;">1.05</td>
<td style="text-align: right;">-3.4</td>
<td style="text-align: right;">0.33</td>
<td style="text-align: right;">2.11</td>
</tr>
<tr>
<td>M5</td>
<td style="text-align: right;">2.67</td>
<td style="text-align: right;">1.86</td>
<td style="text-align: right;"><strong>7.9</strong></td>
<td style="text-align: right;">0.63</td>
<td style="text-align: right;">3.72</td>
</tr>
<tr>
<td>M6</td>
<td style="text-align: right;">2.58</td>
<td style="text-align: right;"><strong>2.33</strong></td>
<td style="text-align: right;">1.8</td>
<td style="text-align: right;">0.60</td>
<td style="text-align: right;">3.19</td>
</tr>
<tr>
<td>M7</td>
<td style="text-align: right;"><strong>2.86</strong></td>
<td style="text-align: right;">2.27</td>
<td style="text-align: right;">5.2</td>
<td style="text-align: right;">0.62</td>
<td style="text-align: right;">3.53</td>
</tr>
<tr>
<td>M8</td>
<td style="text-align: right;">2.61</td>
<td style="text-align: right;">2.05</td>
<td style="text-align: right;">5.9</td>
<td style="text-align: right;"><strong>0.64</strong></td>
<td style="text-align: right;"><strong>3.74</strong></td>
</tr>
</tbody>
</table>
</div>
<h2 id="citation">
Citation
</h2>
<div class="container">
<div class="inner-container" dir="auto" data-snippet-clipboard-copy-content="{% raw %}@article{richter2024investigating,
title={Investigating Training Objectives for Generative Speech Enhancement},
author={Julius Richter and Danilo de Oliveira and Timo Gerkmann},
journal={arXiv preprint arXiv:2409.10753},
year={2024}
}{% endraw %}">
<pre><code>{% raw %}@article{richter2024investigating,
title={Investigating Training Objectives for Generative Speech Enhancement},
author={Julius Richter and Danilo de Oliveira and Timo Gerkmann},
journal={arXiv preprint arXiv:2409.10753},
year={2024}
}{% endraw %}</code></pre>
</div>
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<br>
<h2>
References
</h2>
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"sgmse": "J. Richter, S. Welker, J.-M. Lemercier, B. Lay, and T. Gerkmann, “Speech enhancement and dereverberation with diffusion-based generative models,” IEEE/ACM Transactions on Audio, Speech, and Language Processing, vol. 31, pp. 2351–2364, 2023.",
"sbse": "A. Jukić, R. Korostik, J. Balam, and B. Ginsburg, “Schrödinger bridge for generative speech enhancement,” ISCA Interspeech, pp. 1175-1179, 2024.",
"convtasnet": "Y. Luo and N. Mesgarani, “Conv-TasNet: Surpassing ideal time–frequency magnitude masking for speech separation,” IEEE/ACM Transactions on Audio, Speech, and Language Processing, vol. 27, no. 8, pp. 1256–1266, 2019.",
"metricgan": "S.-W. Fu, C. Yu, T.-A. Hsieh, P. Plantinga, M. Ravanelli, X. Lu, and Y. Tsao, “MetricGAN+: An improved version of MetricGAN for speech enhancement,” ISCA Interspeech, pp. 201-205, 2021.",
"se-mamba": "R. Chao, W.-H. Cheng, M. La Quatra, S.M. Siniscalchi, C.-H.H. Yang, S.-W. Fu, and Y. Tsao, “An investigation of incorporating mamba for speech enhancement,” IEEE Spoken Language Technology Workshop, 2024.",
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