Results per datasets and models under diverse metrics for the extensive search (continued).

<table><caption>**Table C.12:** Results per dataset and model under diverse metrics. The training times (gradient descent) and sampling times are given in seconds. The sampling times are given for 5 samples. The best values per metric are formatted in **bold green** and the worse values are in **red**.</caption><thead><tr><th rowspan="2">Dataset</th><th rowspan="2">Model</th><th colspan="7">Metrics</th></tr><tr><th>C2ST ↓</th><th>DCR-Rate ↓</th><th>ML-Efficacy ↑</th><th>Shape ↑</th><th>Pair ↑</th><th>Train time ↓</th><th>Sample time ↓</th></tr></thead><tbody><tr><td rowspan="6">King</td><td>Train Copy</td><td>0.50 ± 0.01</td><td>1.00 ± 0.00</td><td>0.87 ± 0.00</td><td>0.98 ± 0.01</td><td>0.97 ± 0.01</td><td>-</td><td>-</td></tr><tr><td>CTGAN</td><td>0.93 ± 0.01</td><td>0.62 ± 0.00</td><td>0.72 ± 0.04</td><td>0.97 ± 0.01</td><td>0.94 ± 0.01</td><td>1805 ± 8.66</td><td>00 ± 0.01</td></tr><tr><td>TVAE</td><td>0.94 ± 0.01</td><td>0.61 ± 0.01</td><td>0.81 ± 0.02</td><td>0.94 ± 0.01</td><td>0.94 ± 0.01</td><td>990 ± 6.97</td><td>00 ± 0.00</td></tr><tr><td>TabDDPM</td><td>0.97 ± 0.01</td><td>0.73 ± 0.06</td><td>0.64 ± 0.20</td><td>0.71 ± 0.06</td><td>0.83 ± 0.01</td><td>244 ± 14.03</td><td>06 ± 0.61</td></tr><tr><td>TabSyn</td><td>0.93 ± 0.01</td><td>0.62 ± 0.00</td><td>0.12 ± 0.03</td><td>0.96 ± 0.01</td><td>0.94 ± 0.00</td><td>2717 ± 648.93</td><td>01 ± 0.01</td></tr><tr><td>SMOTE</td><td>0.98 ± 0.00</td><td>0.97 ± 0.00</td><td>0.83 ± 0.01</td><td>0.92 ± 0.01</td><td>0.95 ± 0.01</td><td>-</td><td>02 ± 0.23</td></tr><tr><td colspan="2">UC-SMOTE</td><td>0.98 ± 0.00</td><td>0.96 ± 0.01</td><td>0.82 ± 0.03</td><td>0.92 ± 0.01</td><td>0.96 ± 0.01</td><td>-</td><td>00 ± 0.03</td></tr><tr><td rowspan="6">Miniboo ne</td><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.89 ± 0.01</td><td>0.99 ± 0.00</td><td>0.99 ± 0.01</td><td>-</td><td>-</td></tr><tr><td>CTGAN</td><td>0.91 ± 0.02</td><td>0.60 ± 0.01</td><td>0.83 ± 0.03</td><td>0.96 ± 0.02</td><td>0.58 ± 0.01</td><td>6879 ± 2388.04</td><td>00 ± 0.06</td></tr><tr><td>TVAE</td><td>0.95 ± 0.03</td><td>0.60 ± 0.00</td><td>0.86 ± 0.00</td><td>0.93 ± 0.01</td><td>0.59 ± 0.01</td><td>4876 ± 4730.59</td><td>00 ± 0.05</td></tr><tr><td>TabDDPM</td><td>0.64 ± 0.02</td><td>0.61 ± 0.01</td><td>0.89 ± 0.00</td><td>0.99 ± 0.00</td><td>0.91 ± 0.03</td><td>193 ± 46.01</td><td>23 ± 8.73</td></tr><tr><td>TabSyn</td><td>0.61 ± 0.01</td><td>0.61 ± 0.00</td><td>0.89 ± 0.00</td><td>0.99 ± 0.01</td><td>0.91 ± 0.03</td><td>7861 ± 1700.48</td><td>07 ± 0.08</td></tr><tr><td>SMOTE</td><td>0.83 ± 0.00</td><td>1.00 ± 0.00</td><td>0.89 ± 0.00</td><td>0.97 ± 0.01</td><td>0.99 ± 0.01</td><td>-</td><td>01 ± 0.10</td></tr><tr><td colspan="2">UC-SMOTE</td><td>0.83 ± 0.00</td><td>1.00 ± 0.00</td><td>0.89 ± 0.00</td><td>0.97 ± 0.01</td><td>0.98 ± 0.01</td><td>-</td><td>03 ± 0.04</td></tr><tr><td rowspan="6">Moons</td><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>1.00 ± 0.00</td><td>0.99 ± 0.00</td><td>0.99 ± 0.00</td><td>-</td><td>-</td></tr><tr><td>CTGAN</td><td>0.68 ± 0.01</td><td>0.61 ± 0.01</td><td>1.00 ± 0.00</td><td>0.96 ± 0.01</td><td>0.97 ± 0.01</td><td>2571 ± 967.05</td><td>00 ± 0.02</td></tr><tr><td>TVAE</td><td>0.63 ± 0.01</td><td>0.61 ± 0.02</td><td>1.00 ± 0.00</td><td>0.98 ± 0.00</td><td>0.97 ± 0.00</td><td>752 ± 51.10</td><td>00 ± 0.01</td></tr><tr><td>TabDDPM</td><td>0.52 ± 0.01</td><td>0.61 ± 0.01</td><td>1.00 ± 0.00</td><td>0.99 ± 0.00</td><td>0.99 ± 0.00</td><td>183 ± 92.44</td><td>09 ± 6.74</td></tr><tr><td>TabSyn</td><td>0.54 ± 0.01</td><td>0.61 ± 0.01</td><td>1.00 ± 0.00</td><td>0.99 ± 0.00</td><td>0.99 ± 0.01</td><td>2647 ± 656.79</td><td>01 ± 0.81</td></tr><tr><td>SMOTE</td><td>0.54 ± 0.00</td><td>0.84 ± 0.05</td><td>1.00 ± 0.00</td><td>0.99 ± 0.00</td><td>0.99 ± 0.00</td><td>-</td><td>00 ± 0.02</td></tr><tr><td colspan="2">UC-SMOTE</td><td>0.54 ± 0.01</td><td>0.80 ± 0.03</td><td>1.00 ± 0.00</td><td>0.99 ± 0.00</td><td>0.99 ± 0.01</td><td>-</td><td>00 ± 0.03</td></tr></tbody></table>

## Appendix D. Training and Sampling Impact

We performed large-scale experiments including a quite costly hyperparameter tuning step. Note that the term "costs" in this section refers to the duration, energy consumption, and CO₂ emissions. We evaluate the training and sampling costs of the models with their optimized hyperparameters, as well as the full hyperparameter tuning costs.

### Appendix D.1. Training and Sampling Costs

Due to the massive nature of the experiments, the hyperparameter search could not all be run on the same hardware. We hence estimated the training (gradient descent) cost by running all models on a single Tesla V100-SXM2 32 GB. Table D.13 provides the raw training and sampling energy consumption
Results per datasets and models under diverse metrics for the extensive search (continued).

<table><thead><tr><th rowspan="2">Dataset</th><th rowspan="2">Model</th><th colspan="8">Metrics</th></tr><tr><th>C2ST ↓</th><th>DCR-Rate ↓</th><th>ML-Efficacy ↑</th><th>Shape ↑</th><th>Pair ↑</th><th>Train time ↓</th><th>Sample time ↓</th></tr></thead><tbody><tr><td rowspan="6">Covertype</td><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.90 ± 0.00</td><td>1.00 ± 0.00</td><td>1.00 ± 0.01</td><td>-</td><td>-</td></tr><tr><td>CTGAN</td><td>0.97 ± 0.01</td><td>0.60 ± 0.01</td><td>0.70 ± 0.01</td><td>0.98 ± 0.00</td><td>0.96 ± 0.01</td><td>51644 ± 17257.41</td><td>04 ± 0.60</td></tr><tr><td>TVAE</td><td>0.90 ± 0.01</td><td>0.60 ± 0.00</td><td>0.77 ± 0.01</td><td>0.98 ± 0.00</td><td>0.96 ± 0.01</td><td>23219 ± 18238.02</td><td>01 ± 0.44</td></tr><tr><td>TabDDPM</td><td>0.94 ± 0.01</td><td>0.59 ± 0.04</td><td>0.66 ± 0.04</td><td>0.95 ± 0.01</td><td>0.91 ± 0.01</td><td>868 ± 30.61</td><td>249 ± 25.67</td></tr><tr><td>TabSyn</td><td>0.63 ± 0.02</td><td>0.62 ± 0.01</td><td>0.75 ± 0.02</td><td>0.99 ± 0.00</td><td>0.69 ± 0.00</td><td>4937 ± 1556.02</td><td>03 ± 0.05</td></tr><tr><td>SMOTE</td><td>0.97 ± 0.00</td><td>0.97 ± 0.00</td><td>0.90 ± 0.00</td><td>1.00 ± 0.00</td><td>1.00 ± 0.01</td><td>-</td><td>125 ± 0.69</td></tr><tr><td rowspan="6">Diamonds</td><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.98 ± 0.00</td><td>0.99 ± 0.00</td><td>0.77 ± 0.01</td><td>-</td><td>-</td></tr><tr><td>CTGAN</td><td>0.86 ± 0.01</td><td>0.65 ± 0.01</td><td>0.94 ± 0.01</td><td>0.97 ± 0.01</td><td>0.80 ± 0.04</td><td>3389 ± 2.57</td><td>00 ± 0.01</td></tr><tr><td>TVAE</td><td>0.79 ± 0.03</td><td>0.64 ± 0.00</td><td>0.96 ± 0.01</td><td>0.94 ± 0.01</td><td>0.74 ± 0.04</td><td>1104 ± 637.85</td><td>00 ± 0.02</td></tr><tr><td>TabDDPM</td><td>0.71 ± 0.01</td><td>0.61 ± 0.00</td><td>0.97 ± 0.00</td><td>0.98 ± 0.01</td><td>0.70 ± 0.02</td><td>374 ± 13.27</td><td>16 ± 6.28</td></tr><tr><td>TabSyn</td><td>0.87 ± 0.01</td><td>0.65 ± 0.00</td><td>0.79 ± 0.10</td><td>0.98 ± 0.01</td><td>0.76 ± 0.04</td><td>3255 ± 360.89</td><td>02 ± 1.12</td></tr><tr><td>SMOTE</td><td>0.97 ± 0.00</td><td>0.93 ± 0.01</td><td>0.92 ± 0.01</td><td>0.97 ± 0.00</td><td>0.77 ± 0.02</td><td>-</td><td>03 ± 0.02</td></tr><tr><td rowspan="6">Heloc</td><td>Train Copy</td><td>0.50 ± 0.01</td><td>1.00 ± 0.00</td><td>0.70 ± 0.01</td><td>0.99 ± 0.00</td><td>0.97 ± 0.01</td><td>-</td><td>-</td></tr><tr><td>CTGAN</td><td>0.92 ± 0.01</td><td>0.64 ± 0.01</td><td>0.66 ± 0.05</td><td>0.97 ± 0.01</td><td>0.94 ± 0.02</td><td>4330 ± 3393.17</td><td>00 ± 0.10</td></tr><tr><td>TVAE</td><td>0.87 ± 0.00</td><td>0.66 ± 0.01</td><td>0.70 ± 0.01</td><td>0.95 ± 0.00</td><td>0.94 ± 0.01</td><td>421 ± 249.85</td><td>00 ± 0.00</td></tr><tr><td>TabDDPM</td><td>0.72 ± 0.01</td><td>0.64 ± 0.01</td><td>0.70 ± 0.01</td><td>0.97 ± 0.00</td><td>0.95 ± 0.01</td><td>80 ± 9.69</td><td>01 ± 0.53</td></tr><tr><td>TabSyn</td><td>0.70 ± 0.02</td><td>0.66 ± 0.01</td><td>0.70 ± 0.02</td><td>0.97 ± 0.00</td><td>0.95 ± 0.01</td><td>1870 ± 302.36</td><td>00 ± 0.00</td></tr><tr><td>SMOTE</td><td>0.92 ± 0.01</td><td>1.00 ± 0.00</td><td>0.69 ± 0.01</td><td>0.94 ± 0.00</td><td>0.95 ± 0.01</td><td>-</td><td>00 ± 0.04</td></tr><tr><td rowspan="6">Higgs</td><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.74 ± 0.00</td><td>0.99 ± 0.00</td><td>0.99 ± 0.00</td><td>-</td><td>-</td></tr><tr><td>CTGAN</td><td>0.85 ± 0.02</td><td>0.60 ± 0.00</td><td>0.70 ± 0.01</td><td>0.99 ± 0.01</td><td>0.98 ± 0.00</td><td>12696 ± 4197.49</td><td>00 ± 0.13</td></tr><tr><td>TVAE</td><td>0.92 ± 0.01</td><td>0.60 ± 0.00</td><td>0.70 ± 0.02</td><td>0.94 ± 0.01</td><td>0.98 ± 0.01</td><td>5752 ± 116.50</td><td>00 ± 0.08</td></tr><tr><td>TabDDPM</td><td>0.57 ± 0.00</td><td>0.63 ± 0.00</td><td>0.73 ± 0.00</td><td>0.99 ± 0.00</td><td>0.99 ± 0.00</td><td>223 ± 10.78</td><td>22 ± 2.25</td></tr><tr><td>TabSyn</td><td>0.57 ± 0.01</td><td>0.61 ± 0.00</td><td>0.73 ± 0.00</td><td>0.94 ± 0.00</td><td>0.99 ± 0.00</td><td>7503 ± 2581.02</td><td>04 ± 2.17</td></tr><tr><td>SMOTE</td><td>0.84 ± 0.00</td><td>1.00 ± 0.00</td><td>0.73 ± 0.00</td><td>0.96 ± 0.00</td><td>0.98 ± 0.01</td><td>-</td><td>00 ± 0.05</td></tr><tr><td rowspan="6">House 16h</td><td>Train Copy</td><td>0.50 ± 0.01</td><td>1.00 ± 0.00</td><td>0.64 ± 0.01</td><td>0.99 ± 0.01</td><td>0.99 ± 0.00</td><td>-</td><td>-</td></tr><tr><td>CTGAN</td><td>0.84 ± 0.01</td><td>0.62 ± 0.00</td><td>0.47 ± 0.01</td><td>0.98 ± 0.01</td><td>0.97 ± 0.01</td><td>983 ± 559.75</td><td>00 ± 0.01</td></tr><tr><td>TVAE</td><td>0.82 ± 0.03</td><td>0.61 ± 0.01</td><td>0.48 ± 0.06</td><td>0.95 ± 0.01</td><td>0.98 ± 0.01</td><td>922 ± 6.68</td><td>00 ± 0.01</td></tr><tr><td>TabDDPM</td><td>0.60 ± 0.01</td><td>0.61 ± 0.00</td><td>0.61 ± 0.02</td><td>0.98 ± 0.00</td><td>0.99 ± 0.01</td><td>95 ± 21.99</td><td>02 ± 0.88</td></tr><tr><td>TabSyn</td><td>0.74 ± 0.01</td><td>0.62 ± 0.01</td><td>0.40 ± 0.02</td><td>0.97 ± 0.00</td><td>0.99 ± 0.00</td><td>2370 ± 810.03</td><td>01 ± 0.01</td></tr><tr><td>SMOTE</td><td>0.87 ± 0.00</td><td>0.86 ± 0.05</td><td>0.62 ± 0.01</td><td>0.92 ± 0.01</td><td>0.99 ± 0.00</td><td>-</td><td>00 ± 0.03</td></tr><tr><td rowspan="6">Insurance</td><td>Train Copy</td><td>0.48 ± 0.01</td><td>1.00 ± 0.00</td><td>0.85 ± 0.03</td><td>0.96 ± 0.01</td><td>0.91 ± 0.01</td><td>-</td><td>-</td></tr><tr><td>CTGAN</td><td>0.67 ± 0.03</td><td>0.92 ± 0.01</td><td>0.71 ± 0.01</td><td>0.94 ± 0.00</td><td>0.87 ± 0.02</td><td>265 ± 23.11</td><td>00 ± 0.00</td></tr><tr><td>TVAE</td><td>0.67 ± 0.02</td><td>0.92 ± 0.01</td><td>0.77 ± 0.01</td><td>0.91 ± 0.01</td><td>0.86 ± 0.02</td><td>32 ± 4.50</td><td>00 ± 0.00</td></tr><tr><td>TabDDPM</td><td>0.68 ± 0.02</td><td>0.62 ± 0.01</td><td>0.83 ± 0.03</td><td>0.93 ± 0.02</td><td>0.89 ± 0.02</td><td>181 ± 18.27</td><td>03 ± 1.01</td></tr><tr><td>TabSyn</td><td>0.60 ± 0.02</td><td>0.61 ± 0.02</td><td>0.82 ± 0.00</td><td>0.94 ± 0.01</td><td>0.88 ± 0.00</td><td>1156 ± 74.54</td><td>00 ± 0.03</td></tr><tr><td>SMOTE</td><td>0.68 ± 0.01</td><td>0.80 ± 0.03</td><td>0.81 ± 0.01</td><td>0.94 ± 0.01</td><td>0.87 ± 0.01</td><td>-</td><td>00 ± 0.01</td></tr><tr><td></td><td>UC-SMOTE</td><td>0.67 ± 0.01</td><td>0.85 ± 0.02</td><td>0.80 ± 0.02</td><td>0.93 ± 0.02</td><td>0.87 ± 0.02</td><td>-</td><td>00 ± 0.00</td></tr></tbody></table>
and emissions for reference. All of the TabSyn costs shown are a combination of the VAE cost and the denoiser cost, which are estimated separately and then added together. Also, all TabSyn costs on the *Covertype* dataset are estimated considering the complete dataset size.

<table><thead><tr><th>Dataset</th><th>Model</th><th>Emissions Training ↓</th><th>Energy Training ↓</th><th>Emissions Sampling ↓</th><th>Energy Sampling ↓</th></tr></thead><tbody><tr><td rowspan="5">Abalone</td><td>CTGAN</td><td>3.05±1.77 · 10<sup>-3</sup></td><td>4.53±2.62 · 10<sup>-2</sup></td><td>9.74±2.37 · 10<sup>-8</sup></td><td>1.45±0.35 · 10<sup>-6</sup></td></tr><tr><td>TabDDPM</td><td>9.16±1.42 · 10<sup>-6</sup></td><td>1.36±0.21 · 10<sup>-4</sup></td><td>2.90±0.50 · 10<sup>-5</sup></td><td>4.31±0.74 · 10<sup>-4</sup></td></tr><tr><td>TabSyn</td><td>3.18±0.32 · 10<sup>-4</sup></td><td>4.27±0.32 · 10<sup>-3</sup></td><td>1.49±0.78 · 10<sup>-6</sup></td><td>2.21±1.16 · 10<sup>-5</sup></td></tr><tr><td>TVAE</td><td>5.06±0.13 · 10<sup>-4</sup></td><td>7.51±0.19 · 10<sup>-3</sup></td><td>6.23±2.14 · 10<sup>-8</sup></td><td>9.24±3.17 · 10<sup>-7</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>4.04±0.35 · 10<sup>-7</sup></td><td>5.99±0.51 · 10<sup>-6</sup></td></tr><tr><td rowspan="5">Adult</td><td>CTGAN</td><td>1.24±0.41 · 10<sup>-2</sup></td><td>1.84±0.61 · 10<sup>-1</sup></td><td>9.67±0.41 · 10<sup>-7</sup></td><td>1.43±0.06 · 10<sup>-5</sup></td></tr><tr><td>TabDDPM</td><td>2.68±0.35 · 10<sup>-4</sup></td><td>3.98±0.51 · 10<sup>-3</sup></td><td>8.41±2.01 · 10<sup>-5</sup></td><td>1.25±0.30 · 10<sup>-3</sup></td></tr><tr><td>TabSyn</td><td>1.68±0.72 · 10<sup>-3</sup></td><td>1.42±0.36 · 10<sup>-2</sup></td><td>1.56±0.85 · 10<sup>-5</sup></td><td>2.31±1.26 · 10<sup>-4</sup></td></tr><tr><td>TVAE</td><td>6.30±0.01 · 10<sup>-3</sup></td><td>9.34±0.01 · 10<sup>-2</sup></td><td>3.54±0.07 · 10<sup>-7</sup></td><td>5.25±0.11 · 10<sup>-6</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>2.46±0.04 · 10<sup>-5</sup></td><td>3.66±0.06 · 10<sup>-4</sup></td></tr><tr><td rowspan="5">Bank marketing</td><td>CTGAN</td><td>1.41±0.03 · 10<sup>-2</sup></td><td>2.09±0.04 · 10<sup>-1</sup></td><td>8.88±0.32 · 10<sup>-7</sup></td><td>1.32±0.05 · 10<sup>-5</sup></td></tr><tr><td>TabDDPM</td><td>2.50±0.22 · 10<sup>-4</sup></td><td>3.71±0.33 · 10<sup>-3</sup></td><td>7.81±1.91 · 10<sup>-5</sup></td><td>1.16±0.28 · 10<sup>-3</sup></td></tr><tr><td>TabSyn</td><td>1.06±0.08 · 10<sup>-3</sup></td><td>1.46±0.04 · 10<sup>-2</sup></td><td>1.80±0.02 · 10<sup>-5</sup></td><td>2.67±0.03 · 10<sup>-4</sup></td></tr><tr><td>TVAE</td><td>4.90±2.83 · 10<sup>-3</sup></td><td>7.27±4.19 · 10<sup>-2</sup></td><td>2.84±0.47 · 10<sup>-7</sup></td><td>4.22±0.69 · 10<sup>-6</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>3.46±0.05 · 10<sup>-5</sup></td><td>5.13±0.08 · 10<sup>-4</sup></td></tr><tr><td rowspan="5">Bike sharing</td><td>CTGAN</td><td>1.68±1.03 · 10<sup>-2</sup></td><td>2.50±1.52 · 10<sup>-1</sup></td><td>5.79±2.48 · 10<sup>-7</sup></td><td>8.59±3.68 · 10<sup>-6</sup></td></tr><tr><td>TabDDPM</td><td>8.73±0.70 · 10<sup>-5</sup></td><td>1.30±0.10 · 10<sup>-3</sup></td><td>6.04±0.72 · 10<sup>-5</sup></td><td>8.96±1.07 · 10<sup>-4</sup></td></tr><tr><td>TabSyn</td><td>6.29±1.72 · 10<sup>-4</sup></td><td>8.11±0.27 · 10<sup>-3</sup></td><td>7.02±0.03 · 10<sup>-6</sup></td><td>1.04±0.00 · 10<sup>-4</sup></td></tr><tr><td>TVAE</td><td>2.42±0.07 · 10<sup>-3</sup></td><td>3.59±0.11 · 10<sup>-2</sup></td><td>1.37±0.27 · 10<sup>-7</sup></td><td>2.03±0.40 · 10<sup>-6</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>4.53±0.22 · 10<sup>-6</sup></td><td>6.72±0.33 · 10<sup>-5</sup></td></tr><tr><td rowspan="5">Black friday</td><td>CTGAN</td><td>4.55±3.60 · 10<sup>-2</sup></td><td>6.75±5.34 · 10<sup>-1</sup></td><td>2.70±0.56 · 10<sup>-6</sup></td><td>4.01±0.83 · 10<sup>-5</sup></td></tr><tr><td>TabDDPM</td><td>8.97±1.75 · 10<sup>-4</sup></td><td>1.33±0.26 · 10<sup>-2</sup></td><td>2.98±1.09 · 10<sup>-4</sup></td><td>4.42±1.62 · 10<sup>-3</sup></td></tr><tr><td>TabSyn</td><td>2.78±0.26 · 10<sup>-3</sup></td><td>2.58±0.90 · 10<sup>-2</sup></td><td>5.18±2.81 · 10<sup>-5</sup></td><td>7.69±4.17 · 10<sup>-4</sup></td></tr><tr><td>TVAE</td><td>2.23±0.01 · 10<sup>-2</sup></td><td>3.31±0.01 · 10<sup>-1</sup></td><td>8.59±0.65 · 10<sup>-7</sup></td><td>1.27±0.10 · 10<sup>-5</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>1.14±0.01 · 10<sup>-4</sup></td><td>1.68±0.01 · 10<sup>-3</sup></td></tr><tr><td rowspan="5">Cardio</td><td>CTGAN</td><td>2.11±0.03 · 10<sup>-2</sup></td><td>3.13±0.04 · 10<sup>-1</sup></td><td>1.30±0.03 · 10<sup>-6</sup></td><td>1.93±0.04 · 10<sup>-5</sup></td></tr><tr><td>TabDDPM</td><td>2.22±1.13 · 10<sup>-4</sup></td><td>3.30±1.68 · 10<sup>-3</sup></td><td>1.05±0.70 · 10<sup>-4</sup></td><td>1.56±1.04 · 10<sup>-3</sup></td></tr><tr><td>TabSyn</td><td>1.15±0.16 · 10<sup>-3</sup></td><td>1.67±0.03 · 10<sup>-2</sup></td><td>2.89±0.01 · 10<sup>-5</sup></td><td>4.29±0.02 · 10<sup>-4</sup></td></tr><tr><td>TVAE</td><td>7.64±4.39 · 10<sup>-3</sup></td><td>1.13±0.65 · 10<sup>-1</sup></td><td>2.70±0.94 · 10<sup>-7</sup></td><td>4.00±1.40 · 10<sup>-6</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>2.27±0.05 · 10<sup>-6</sup></td><td>3.37±0.07 · 10<sup>-5</sup></td></tr><tr><td rowspan="5">Churn</td><td>CTGAN</td><td>1.15±0.43 · 10<sup>-2</sup></td><td>1.71±0.63 · 10<sup>-1</sup></td><td>6.61±1.15 · 10<sup>-7</sup></td><td>9.81±1.71 · 10<sup>-6</sup></td></tr><tr><td>TabDDPM</td><td>1.10±0.07 · 10<sup>-4</sup></td><td>1.63±0.10 · 10<sup>-3</sup></td><td>1.96±0.17 · 10<sup>-4</sup></td><td>2.90±0.25 · 10<sup>-3</sup></td></tr><tr><td>TabSyn</td><td>4.97±0.79 · 10<sup>-4</sup></td><td>6.25±0.62 · 10<sup>-3</sup></td><td>3.43±1.81 · 10<sup>-6</sup></td><td>5.09±2.68 · 10<sup>-5</sup></td></tr><tr><td>TVAE</td><td>1.34±0.03 · 10<sup>-3</sup></td><td>1.98±0.05 · 10<sup>-2</sup></td><td>3.08±0.29 · 10<sup>-7</sup></td><td>4.57±0.42 · 10<sup>-6</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>4.13±0.20 · 10<sup>-6</sup></td><td>6.12±0.29 · 10<sup>-5</sup></td></tr><tr><td></td><td>UC-SMOTE</td><td>-</td><td>-</td><td>3.53±0.19 · 10<sup>-6</sup></td><td>5.24±0.28 · 10<sup>-5</sup></td></tr></tbody></table>
Results per datasets and models under diverse metrics for the extensive search (continued).

<table><caption>**Table C.12:** Results per dataset and model under diverse metrics. The training times (gradient descent) and sampling times are given in seconds. The sampling times are given for 5 samples. The best values per metric are formatted in **bold green** and the worse values are in **red**.</caption><thead><tr><th rowspan="2">Dataset</th><th rowspan="2">Model</th><th colspan="7">Metrics</th></tr><tr><th>C2ST ↓</th><th>DCR-Rate ↓</th><th>ML-Efficacy ↑</th><th>Shape ↑</th><th>Pair ↑</th><th>Train time ↓</th><th>Sample time ↓</th></tr></thead><tbody><tr><td rowspan="6">King</td><td>Train Copy</td><td>0.50 ± 0.01</td><td>1.00 ± 0.00</td><td>0.87 ± 0.00</td><td>0.98 ± 0.01</td><td>0.97 ± 0.01</td><td>-</td><td>-</td></tr><tr><td>CTGAN</td><td>0.93 ± 0.01</td><td>0.62 ± 0.00</td><td>0.72 ± 0.04</td><td>0.97 ± 0.01</td><td>0.94 ± 0.01</td><td>1805 ± 8.66</td><td>00 ± 0.01</td></tr><tr><td>TVAE</td><td>0.94 ± 0.01</td><td>0.61 ± 0.01</td><td>0.81 ± 0.02</td><td>0.94 ± 0.01</td><td>0.94 ± 0.01</td><td>990 ± 6.97</td><td>00 ± 0.00</td></tr><tr><td>TabDDPM</td><td>0.97 ± 0.01</td><td>0.73 ± 0.06</td><td>0.64 ± 0.20</td><td>0.71 ± 0.06</td><td>0.83 ± 0.01</td><td>244 ± 14.03</td><td>06 ± 0.61</td></tr><tr><td>TabSyn</td><td>0.93 ± 0.01</td><td>0.62 ± 0.00</td><td>0.12 ± 0.03</td><td>0.96 ± 0.01</td><td>0.94 ± 0.00</td><td>2717 ± 648.93</td><td>01 ± 0.01</td></tr><tr><td>SMOTE</td><td>0.98 ± 0.00</td><td>0.97 ± 0.00</td><td>0.83 ± 0.01</td><td>0.92 ± 0.01</td><td>0.95 ± 0.01</td><td>-</td><td>02 ± 0.23</td></tr><tr><td rowspan="6">Miniboo ne</td><td>UC-SMOTE</td><td>0.98 ± 0.00</td><td>0.96 ± 0.01</td><td>0.82 ± 0.03</td><td>0.92 ± 0.01</td><td>0.96 ± 0.01</td><td>-</td><td>00 ± 0.03</td></tr><tr><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.89 ± 0.01</td><td>0.99 ± 0.00</td><td>0.99 ± 0.01</td><td>-</td><td>-</td></tr><tr><td>CTGAN</td><td>0.91 ± 0.02</td><td>0.60 ± 0.01</td><td>0.83 ± 0.03</td><td>0.96 ± 0.02</td><td>0.58 ± 0.01</td><td>6879 ± 2388.04</td><td>00 ± 0.06</td></tr><tr><td>TVAE</td><td>0.95 ± 0.03</td><td>0.60 ± 0.00</td><td>0.86 ± 0.00</td><td>0.93 ± 0.01</td><td>0.59 ± 0.01</td><td>4876 ± 4730.59</td><td>00 ± 0.05</td></tr><tr><td>TabDDPM</td><td>0.64 ± 0.02</td><td>0.61 ± 0.01</td><td>0.89 ± 0.00</td><td>0.99 ± 0.00</td><td>0.91 ± 0.03</td><td>193 ± 46.01</td><td>23 ± 8.73</td></tr><tr><td>TabSyn</td><td>0.61 ± 0.01</td><td>0.61 ± 0.00</td><td>0.89 ± 0.00</td><td>0.99 ± 0.01</td><td>0.91 ± 0.03</td><td>7861 ± 1700.48</td><td>07 ± 0.08</td></tr><tr><td rowspan="6">Moons</td><td>SMOTE</td><td>0.83 ± 0.00</td><td>1.00 ± 0.00</td><td>0.89 ± 0.00</td><td>0.97 ± 0.01</td><td>0.99 ± 0.01</td><td>-</td><td>01 ± 0.10</td></tr><tr><td>UC-SMOTE</td><td>0.83 ± 0.00</td><td>1.00 ± 0.00</td><td>0.89 ± 0.00</td><td>0.97 ± 0.01</td><td>0.98 ± 0.01</td><td>-</td><td>03 ± 0.04</td></tr><tr><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>1.00 ± 0.00</td><td>0.99 ± 0.00</td><td>0.99 ± 0.00</td><td>-</td><td>-</td></tr><tr><td>CTGAN</td><td>0.68 ± 0.01</td><td>0.61 ± 0.01</td><td>1.00 ± 0.00</td><td>0.96 ± 0.01</td><td>0.97 ± 0.01</td><td>2571 ± 967.05</td><td>00 ± 0.02</td></tr><tr><td>TVAE</td><td>0.63 ± 0.01</td><td>0.61 ± 0.02</td><td>1.00 ± 0.00</td><td>0.98 ± 0.00</td><td>0.97 ± 0.00</td><td>752 ± 51.10</td><td>00 ± 0.01</td></tr><tr><td>TabDDPM</td><td>0.52 ± 0.01</td><td>0.61 ± 0.01</td><td>1.00 ± 0.00</td><td>0.99 ± 0.00</td><td>0.99 ± 0.00</td><td>183 ± 92.44</td><td>09 ± 6.74</td></tr><tr><td rowspan="6">UC-SMOTE</td><td>TabSyn</td><td>0.54 ± 0.01</td><td>0.61 ± 0.01</td><td>1.00 ± 0.00</td><td>0.99 ± 0.00</td><td>0.99 ± 0.01</td><td>2647 ± 656.79</td><td>01 ± 0.81</td></tr><tr><td>SMOTE</td><td>0.54 ± 0.00</td><td>0.84 ± 0.05</td><td>1.00 ± 0.00</td><td>0.99 ± 0.00</td><td>0.99 ± 0.00</td><td>-</td><td>00 ± 0.02</td></tr><tr><td>UC-SMOTE</td><td>0.54 ± 0.01</td><td>0.80 ± 0.03</td><td>1.00 ± 0.00</td><td>0.99 ± 0.00</td><td>0.99 ± 0.01</td><td>-</td><td>00 ± 0.03</td></tr></tbody></table>

## Appendix D. Training and Sampling Impact

We performed large-scale experiments including a quite costly hyperparameter tuning step. Note that the term "costs" in this section refers to the duration, energy consumption, and CO₂ emissions. We evaluate the training and sampling costs of the models with their optimized hyperparameters, as well as the full hyperparameter tuning costs.

### Appendix D.1. Training and Sampling Costs

Due to the massive nature of the experiments, the hyperparameter search could not all be run on the same hardware. We hence estimated the training (gradient descent) cost by running all models on a single Tesla V100-SXM2 32 GB. Table D.13 provides the raw training and sampling energy consumption
Tuning costs estimation for the best models (continued).

<table><thead><tr><th>Dataset</th><th>Model</th><th>Emissions Training ↓</th><th>Energy Training ↓</th><th>Emissions Sampling ↓</th><th>Energy Sampling ↓</th></tr></thead><tbody><tr><td rowspan="6">Covertype</td><td>CTGAN</td><td>2.33±0.78 · 10<sup>-1</sup></td><td>3.46±1.15</td><td>1.92±0.27 · 10<sup>-5</sup></td><td>2.85±0.41 · 10<sup>-4</sup></td></tr><tr><td>TabDDPM</td><td>6.22±0.35 · 10<sup>-3</sup></td><td>9.23±0.53 · 10<sup>-2</sup></td><td>1.80±0.26 · 10<sup>-3</sup></td><td>2.67±0.38 · 10<sup>-2</sup></td></tr><tr><td>TabSyn</td><td>1.82±0.68 · 10<sup>-3</sup></td><td>1.26±0.72 · 10<sup>-2</sup></td><td>2.37±0.04 · 10<sup>-5</sup></td><td>3.52±0.06 · 10<sup>-4</sup></td></tr><tr><td>TVAE</td><td>1.04±0.81 · 10<sup>-1</sup></td><td>1.54±1.21</td><td>8.00±1.93 · 10<sup>-6</sup></td><td>1.19±0.29 · 10<sup>-4</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>4.52±0.02 · 10<sup>-4</sup></td><td>6.71±0.04 · 10<sup>-3</sup></td></tr><tr><td>UC-SMOTE</td><td>-</td><td>-</td><td>5.01±0.03 · 10<sup>-4</sup></td><td>7.43±0.04 · 10<sup>-3</sup></td></tr><tr><td rowspan="6">Diamonds</td><td>CTGAN</td><td>1.52±0.00 · 10<sup>-2</sup></td><td>2.26±0.01 · 10<sup>-1</sup></td><td>8.44±0.13 · 10<sup>-7</sup></td><td>1.25±0.02 · 10<sup>-5</sup></td></tr><tr><td>TabDDPM</td><td>3.33±0.71 · 10<sup>-4</sup></td><td>4.93±1.06 · 10<sup>-3</sup></td><td>1.30±0.47 · 10<sup>-4</sup></td><td>1.92±0.70 · 10<sup>-3</sup></td></tr><tr><td>TabSyn</td><td>1.21±0.18 · 10<sup>-3</sup></td><td>1.36±0.49 · 10<sup>-2</sup></td><td>1.67±0.89 · 10<sup>-5</sup></td><td>2.48±1.32 · 10<sup>-4</sup></td></tr><tr><td>TVAE</td><td>4.93±2.84 · 10<sup>-3</sup></td><td>7.31±4.21 · 10<sup>-2</sup></td><td>2.42±0.76 · 10<sup>-7</sup></td><td>3.59±1.12 · 10<sup>-6</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>1.32±0.01 · 10<sup>-5</sup></td><td>1.96±0.01 · 10<sup>-4</sup></td></tr><tr><td>UC-SMOTE</td><td>-</td><td>-</td><td>3.67±0.14 · 10<sup>-6</sup></td><td>5.44±0.21 · 10<sup>-5</sup></td></tr><tr><td rowspan="6">Heloc</td><td>CTGAN</td><td>1.93±1.51 · 10<sup>-2</sup></td><td>2.87±2.24 · 10<sup>-1</sup></td><td>6.03±4.19 · 10<sup>-7</sup></td><td>8.95±6.22 · 10<sup>-6</sup></td></tr><tr><td>TabDDPM</td><td>1.21±0.29 · 10<sup>-5</sup></td><td>1.80±0.43 · 10<sup>-4</sup></td><td>1.50±0.42 · 10<sup>-5</sup></td><td>2.23±0.63 · 10<sup>-4</sup></td></tr><tr><td>TabSyn</td><td>5.78±0.66 · 10<sup>-4</sup></td><td>6.91±0.18 · 10<sup>-3</sup></td><td>4.60±0.11 · 10<sup>-6</sup></td><td>6.83±0.16 · 10<sup>-5</sup></td></tr><tr><td>TVAE</td><td>1.88±1.11 · 10<sup>-3</sup></td><td>2.80±1.65 · 10<sup>-2</sup></td><td>1.15±0.43 · 10<sup>-7</sup></td><td>1.71±0.63 · 10<sup>-6</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>9.32±1.28 · 10<sup>-7</sup></td><td>1.38±0.19 · 10<sup>-5</sup></td></tr><tr><td>UC-SMOTE</td><td>-</td><td>-</td><td>2.02±0.07 · 10<sup>-6</sup></td><td>3.00±0.10 · 10<sup>-5</sup></td></tr><tr><td rowspan="6">Higgs</td><td>CTGAN</td><td>5.71±1.88 · 10<sup>-2</sup></td><td>8.47±2.79 · 10<sup>-1</sup></td><td>2.92±0.56 · 10<sup>-6</sup></td><td>4.33±0.84 · 10<sup>-5</sup></td></tr><tr><td>TabDDPM</td><td>4.01±0.25 · 10<sup>-4</sup></td><td>5.96±0.37 · 10<sup>-3</sup></td><td>1.77±0.18 · 10<sup>-4</sup></td><td>2.63±0.27 · 10<sup>-3</sup></td></tr><tr><td>TabSyn</td><td>2.88±1.12 · 10<sup>-3</sup></td><td>2.07±0.74 · 10<sup>-2</sup></td><td>3.20±1.72 · 10<sup>-5</sup></td><td>4.75±2.55 · 10<sup>-4</sup></td></tr><tr><td>TVAE</td><td>2.57±0.05 · 10<sup>-2</sup></td><td>3.81±0.08 · 10<sup>-1</sup></td><td>1.06±0.34 · 10<sup>-6</sup></td><td>1.58±0.51 · 10<sup>-5</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>2.01±0.19 · 10<sup>-6</sup></td><td>2.98±0.28 · 10<sup>-5</sup></td></tr><tr><td>UC-SMOTE</td><td>-</td><td>-</td><td>6.19±0.13 · 10<sup>-6</sup></td><td>9.18±0.20 · 10<sup>-5</sup></td></tr><tr><td rowspan="6">House 16h</td><td>CTGAN</td><td>4.42±2.48 · 10<sup>-3</sup></td><td>6.55±3.68 · 10<sup>-2</sup></td><td>1.24±0.16 · 10<sup>-7</sup></td><td>1.85±0.24 · 10<sup>-6</sup></td></tr><tr><td>TabDDPM</td><td>3.81±1.14 · 10<sup>-5</sup></td><td>5.66±1.69 · 10<sup>-4</sup></td><td>2.03±0.70 · 10<sup>-5</sup></td><td>3.01±1.04 · 10<sup>-4</sup></td></tr><tr><td>TabSyn</td><td>8.56±2.73 · 10<sup>-4</sup></td><td>9.40±1.12 · 10<sup>-3</sup></td><td>9.68±0.08 · 10<sup>-6</sup></td><td>1.44±0.01 · 10<sup>-4</sup></td></tr><tr><td>TVAE</td><td>4.12±0.02 · 10<sup>-3</sup></td><td>6.11±0.03 · 10<sup>-2</sup></td><td>1.40±0.17 · 10<sup>-7</sup></td><td>2.08±0.26 · 10<sup>-6</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>2.92±1.19 · 10<sup>-7</sup></td><td>4.34±1.77 · 10<sup>-6</sup></td></tr><tr><td>UC-SMOTE</td><td>-</td><td>-</td><td>4.04±0.48 · 10<sup>-7</sup></td><td>5.99±0.72 · 10<sup>-6</sup></td></tr><tr><td rowspan="6">Insurance</td><td>CTGAN</td><td>1.18±0.10 · 10<sup>-3</sup></td><td>1.75±0.15 · 10<sup>-2</sup></td><td>7.40±1.62 · 10<sup>-8</sup></td><td>1.10±0.24 · 10<sup>-6</sup></td></tr><tr><td>TabDDPM</td><td>2.83±0.29 · 10<sup>-6</sup></td><td>4.20±0.43 · 10<sup>-5</sup></td><td>2.65±0.94 · 10<sup>-5</sup></td><td>3.93±1.40 · 10<sup>-4</sup></td></tr><tr><td>TabSyn</td><td>3.45±0.04 · 10<sup>-4</sup></td><td>4.64±0.36 · 10<sup>-3</sup></td><td>5.87±2.03 · 10<sup>-7</sup></td><td>8.71±3.01 · 10<sup>-6</sup></td></tr><tr><td>TVAE</td><td>1.44±0.20 · 10<sup>-4</sup></td><td>2.14±0.29 · 10<sup>-3</sup></td><td>4.70±1.02 · 10<sup>-8</sup></td><td>6.98±1.51 · 10<sup>-7</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>1.83±0.26 · 10<sup>-7</sup></td><td>2.71±0.39 · 10<sup>-6</sup></td></tr><tr><td>UC-SMOTE</td><td>-</td><td>-</td><td>1.02±0.04 · 10<sup>-7</sup></td><td>1.51±0.06 · 10<sup>-6</sup></td></tr><tr><td rowspan="6">King</td><td>CTGAN</td><td>8.15±0.04 · 10<sup>-3</sup></td><td>1.21±0.01 · 10<sup>-1</sup></td><td>5.72±0.34 · 10<sup>-7</sup></td><td>8.49±0.50 · 10<sup>-6</sup></td></tr><tr><td>TabDDPM</td><td>9.27±0.56 · 10<sup>-5</sup></td><td>1.38±0.08 · 10<sup>-3</sup></td><td>5.08±0.49 · 10<sup>-5</sup></td><td>7.55±0.73 · 10<sup>-4</sup></td></tr><tr><td>TabSyn</td><td>9.40±1.26 · 10<sup>-4</sup></td><td>9.57±0.35 · 10<sup>-3</sup></td><td>9.15±0.02 · 10<sup>-6</sup></td><td>1.36±0.00 · 10<sup>-4</sup></td></tr><tr><td>TVAE</td><td>4.43±0.04 · 10<sup>-3</sup></td><td>6.57±0.07 · 10<sup>-2</sup></td><td>2.59±0.18 · 10<sup>-7</sup></td><td>3.85±0.26 · 10<sup>-6</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>8.77±0.84 · 10<sup>-6</sup></td><td>1.30±0.12 · 10<sup>-4</sup></td></tr><tr><td>UC-SMOTE</td><td>-</td><td>-</td><td>2.25±0.10 · 10<sup>-6</sup></td><td>3.34±0.14 · 10<sup>-5</sup></td></tr></tbody></table>
and emissions for reference. All of the TabSyn costs shown are a combination of the VAE cost and the denoiser cost, which are estimated separately and then added together. Also, all TabSyn costs on the *Covertype* dataset are estimated considering the complete dataset size.

<table><thead><tr><th>Dataset</th><th>Model</th><th>Emissions Training ↓</th><th>Energy Training ↓</th><th>Emissions Sampling ↓</th><th>Energy Sampling ↓</th></tr></thead><tbody><tr><td rowspan="5">Abalone</td><td>CTGAN</td><td>3.05±1.77 · 10<sup>-3</sup></td><td>4.53±2.62 · 10<sup>-2</sup></td><td>9.74±2.37 · 10<sup>-8</sup></td><td>1.45±0.35 · 10<sup>-6</sup></td></tr><tr><td>TabDDPM</td><td>9.16±1.42 · 10<sup>-6</sup></td><td>1.36±0.21 · 10<sup>-4</sup></td><td>2.90±0.50 · 10<sup>-5</sup></td><td>4.31±0.74 · 10<sup>-4</sup></td></tr><tr><td>TabSyn</td><td>3.18±0.32 · 10<sup>-4</sup></td><td>4.27±0.32 · 10<sup>-3</sup></td><td>1.49±0.78 · 10<sup>-6</sup></td><td>2.21±1.16 · 10<sup>-5</sup></td></tr><tr><td>TVAE</td><td>5.06±0.13 · 10<sup>-4</sup></td><td>7.51±0.19 · 10<sup>-3</sup></td><td>6.23±2.14 · 10<sup>-8</sup></td><td>9.24±3.17 · 10<sup>-7</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>4.04±0.35 · 10<sup>-7</sup></td><td>5.99±0.51 · 10<sup>-6</sup></td></tr><tr><td rowspan="5">Adult</td><td>CTGAN</td><td>1.24±0.41 · 10<sup>-2</sup></td><td>1.84±0.61 · 10<sup>-1</sup></td><td>9.67±0.41 · 10<sup>-7</sup></td><td>1.43±0.06 · 10<sup>-5</sup></td></tr><tr><td>TabDDPM</td><td>2.68±0.35 · 10<sup>-4</sup></td><td>3.98±0.51 · 10<sup>-3</sup></td><td>8.41±2.01 · 10<sup>-5</sup></td><td>1.25±0.30 · 10<sup>-3</sup></td></tr><tr><td>TabSyn</td><td>1.68±0.72 · 10<sup>-3</sup></td><td>1.42±0.36 · 10<sup>-2</sup></td><td>1.56±0.85 · 10<sup>-5</sup></td><td>2.31±1.26 · 10<sup>-4</sup></td></tr><tr><td>TVAE</td><td>6.30±0.01 · 10<sup>-3</sup></td><td>9.34±0.01 · 10<sup>-2</sup></td><td>3.54±0.07 · 10<sup>-7</sup></td><td>5.25±0.11 · 10<sup>-6</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>2.46±0.04 · 10<sup>-5</sup></td><td>3.66±0.06 · 10<sup>-4</sup></td></tr><tr><td rowspan="5">Bank marketing</td><td>CTGAN</td><td>1.41±0.03 · 10<sup>-2</sup></td><td>2.09±0.04 · 10<sup>-1</sup></td><td>8.88±0.32 · 10<sup>-7</sup></td><td>1.32±0.05 · 10<sup>-5</sup></td></tr><tr><td>TabDDPM</td><td>2.50±0.22 · 10<sup>-4</sup></td><td>3.71±0.33 · 10<sup>-3</sup></td><td>7.81±1.91 · 10<sup>-5</sup></td><td>1.16±0.28 · 10<sup>-3</sup></td></tr><tr><td>TabSyn</td><td>1.06±0.08 · 10<sup>-3</sup></td><td>1.46±0.04 · 10<sup>-2</sup></td><td>1.80±0.02 · 10<sup>-5</sup></td><td>2.67±0.03 · 10<sup>-4</sup></td></tr><tr><td>TVAE</td><td>4.90±2.83 · 10<sup>-3</sup></td><td>7.27±4.19 · 10<sup>-2</sup></td><td>2.84±0.47 · 10<sup>-7</sup></td><td>4.22±0.69 · 10<sup>-6</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>3.46±0.05 · 10<sup>-5</sup></td><td>5.13±0.08 · 10<sup>-4</sup></td></tr><tr><td rowspan="5">Bike sharing</td><td>CTGAN</td><td>1.68±1.03 · 10<sup>-2</sup></td><td>2.50±1.52 · 10<sup>-1</sup></td><td>5.79±2.48 · 10<sup>-7</sup></td><td>8.59±3.68 · 10<sup>-6</sup></td></tr><tr><td>TabDDPM</td><td>8.73±0.70 · 10<sup>-5</sup></td><td>1.30±0.10 · 10<sup>-3</sup></td><td>6.04±0.72 · 10<sup>-5</sup></td><td>8.96±1.07 · 10<sup>-4</sup></td></tr><tr><td>TabSyn</td><td>6.29±1.72 · 10<sup>-4</sup></td><td>8.11±0.27 · 10<sup>-3</sup></td><td>7.02±0.03 · 10<sup>-6</sup></td><td>1.04±0.00 · 10<sup>-4</sup></td></tr><tr><td>TVAE</td><td>2.42±0.07 · 10<sup>-3</sup></td><td>3.59±0.11 · 10<sup>-2</sup></td><td>1.37±0.27 · 10<sup>-7</sup></td><td>2.03±0.40 · 10<sup>-6</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>4.53±0.22 · 10<sup>-6</sup></td><td>6.72±0.33 · 10<sup>-5</sup></td></tr><tr><td rowspan="5">Black friday</td><td>CTGAN</td><td>4.55±3.60 · 10<sup>-2</sup></td><td>6.75±5.34 · 10<sup>-1</sup></td><td>2.70±0.56 · 10<sup>-6</sup></td><td>4.01±0.83 · 10<sup>-5</sup></td></tr><tr><td>TabDDPM</td><td>8.97±1.75 · 10<sup>-4</sup></td><td>1.33±0.26 · 10<sup>-2</sup></td><td>2.98±1.09 · 10<sup>-4</sup></td><td>4.42±1.62 · 10<sup>-3</sup></td></tr><tr><td>TabSyn</td><td>2.78±0.26 · 10<sup>-3</sup></td><td>2.58±0.90 · 10<sup>-2</sup></td><td>5.18±2.81 · 10<sup>-5</sup></td><td>7.69±4.17 · 10<sup>-4</sup></td></tr><tr><td>TVAE</td><td>2.23±0.01 · 10<sup>-2</sup></td><td>3.31±0.01 · 10<sup>-1</sup></td><td>8.59±0.65 · 10<sup>-7</sup></td><td>1.27±0.10 · 10<sup>-5</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>1.14±0.01 · 10<sup>-4</sup></td><td>1.68±0.01 · 10<sup>-3</sup></td></tr><tr><td rowspan="5">Cardio</td><td>CTGAN</td><td>2.11±0.03 · 10<sup>-2</sup></td><td>3.13±0.04 · 10<sup>-1</sup></td><td>1.30±0.03 · 10<sup>-6</sup></td><td>1.93±0.04 · 10<sup>-5</sup></td></tr><tr><td>TabDDPM</td><td>2.22±1.13 · 10<sup>-4</sup></td><td>3.30±1.68 · 10<sup>-3</sup></td><td>1.05±0.70 · 10<sup>-4</sup></td><td>1.56±1.04 · 10<sup>-3</sup></td></tr><tr><td>TabSyn</td><td>1.15±0.16 · 10<sup>-3</sup></td><td>1.67±0.03 · 10<sup>-2</sup></td><td>2.89±0.01 · 10<sup>-5</sup></td><td>4.29±0.02 · 10<sup>-4</sup></td></tr><tr><td>TVAE</td><td>7.64±4.39 · 10<sup>-3</sup></td><td>1.13±0.65 · 10<sup>-1</sup></td><td>2.70±0.94 · 10<sup>-7</sup></td><td>4.00±1.40 · 10<sup>-6</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>2.27±0.05 · 10<sup>-6</sup></td><td>3.37±0.07 · 10<sup>-5</sup></td></tr><tr><td rowspan="5">Churn</td><td>CTGAN</td><td>1.15±0.43 · 10<sup>-2</sup></td><td>1.71±0.63 · 10<sup>-1</sup></td><td>6.61±1.15 · 10<sup>-7</sup></td><td>9.81±1.71 · 10<sup>-6</sup></td></tr><tr><td>TabDDPM</td><td>1.10±0.07 · 10<sup>-4</sup></td><td>1.63±0.10 · 10<sup>-3</sup></td><td>1.96±0.17 · 10<sup>-4</sup></td><td>2.90±0.25 · 10<sup>-3</sup></td></tr><tr><td>TabSyn</td><td>4.97±0.79 · 10<sup>-4</sup></td><td>6.25±0.62 · 10<sup>-3</sup></td><td>3.43±1.81 · 10<sup>-6</sup></td><td>5.09±2.68 · 10<sup>-5</sup></td></tr><tr><td>TVAE</td><td>1.34±0.03 · 10<sup>-3</sup></td><td>1.98±0.05 · 10<sup>-2</sup></td><td>3.08±0.29 · 10<sup>-7</sup></td><td>4.57±0.42 · 10<sup>-6</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>4.13±0.20 · 10<sup>-6</sup></td><td>6.12±0.29 · 10<sup>-5</sup></td></tr><tr><td></td><td>UC-SMOTE</td><td>-</td><td>-</td><td>3.53±0.19 · 10<sup>-6</sup></td><td>5.24±0.28 · 10<sup>-5</sup></td></tr></tbody></table>
Tuning costs estimation for the best models (continued).

<table><caption>**Table D.13:** CO₂ emissions (in Kg) and Energy Consumption (in kWh) of the benchmark challengers. The energy consumption is obtained by summing the CPU, GPU and RAM energy. Training costs are given for all models on the same basis of 400 epochs. Sampling costs are given for 5 samples. The best values are formatted in **bold green** and the worse are in **red**.</caption><thead><tr><th>Dataset</th><th>Model</th><th>Emissions Training ↓</th><th>Energy Training ↓</th><th>Emissions Sampling ↓</th><th>Energy Sampling ↓</th></tr></thead><tbody><tr><td rowspan="6">Minibootne</td><td>CTGAN</td><td>3.16±1.09 · 10<sup>-2</sup></td><td>4.69±1.62 · 10<sup>-1</sup></td><td>3.50±0.24 · 10<sup>-6</sup></td><td>5.20±0.35 · 10<sup>-5</sup></td></tr><tr><td>TabDDPM</td><td>4.50±1.33 · 10<sup>-4</sup></td><td>6.68±1.97 · 10<sup>-3</sup></td><td>1.84±0.69 · 10<sup>-4</sup></td><td>2.74±1.03 · 10<sup>-3</sup></td></tr><tr><td>TabSyn</td><td>3.41±0.61 · 10<sup>-3</sup></td><td>3.18±0.79 · 10<sup>-2</sup></td><td>5.57±0.07 · 10<sup>-5</sup></td><td>8.26±0.11 · 10<sup>-4</sup></td></tr><tr><td>TVAE</td><td>2.18±2.12 · 10<sup>-2</sup></td><td>3.24±3.14 · 10<sup>-1</sup></td><td>1.94±0.22 · 10<sup>-6</sup></td><td>2.88±0.32 · 10<sup>-5</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>4.39±0.34 · 10<sup>-6</sup></td><td>6.51±0.51 · 10<sup>-5</sup></td></tr><tr><td>UC-SMOTE</td><td>-</td><td>-</td><td>1.32±0.01 · 10<sup>-5</sup></td><td>1.95±0.02 · 10<sup>-4</sup></td></tr><tr><td rowspan="6">Moons</td><td>CTGAN</td><td>1.15±0.43 · 10<sup>-2</sup></td><td>1.71±0.64 · 10<sup>-1</sup></td><td>5.02±1.07 · 10<sup>-7</sup></td><td>7.45±1.59 · 10<sup>-6</sup></td></tr><tr><td>TabDDPM</td><td>1.31±0.77 · 10<sup>-4</sup></td><td>1.94±1.14 · 10<sup>-3</sup></td><td>7.39±5.33 · 10<sup>-5</sup></td><td>1.10±0.79 · 10<sup>-3</sup></td></tr><tr><td>TabSyn</td><td>9.26±2.41 · 10<sup>-4</sup></td><td>1.14±0.36 · 10<sup>-2</sup></td><td>1.22±0.65 · 10<sup>-5</sup></td><td>1.81±0.96 · 10<sup>-4</sup></td></tr><tr><td>TVAE</td><td>3.37±0.24 · 10<sup>-3</sup></td><td>5.00±0.36 · 10<sup>-2</sup></td><td>1.78±0.43 · 10<sup>-7</sup></td><td>2.65±0.64 · 10<sup>-6</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>2.44±0.52 · 10<sup>-7</sup></td><td>3.63±0.78 · 10<sup>-6</sup></td></tr><tr><td>UC-SMOTE</td><td>-</td><td>-</td><td>1.03±0.12 · 10<sup>-6</sup></td><td>1.53±0.18 · 10<sup>-5</sup></td></tr></tbody></table>

## Appendix D.2. Whole Tuning Cost Estimation

As mentioned in Section 3.1 we could not perform the hyperparameter search and training phases on a uniform hardware and software architecture and we estimated the tuning cost with Equation (1).

Each trial can be stopped based on three conditions: an early stopping decided by the model, a poor C2ST performance or a time limit. Therefore, to get an accurate estimate of the init-cost and the cost-per-step from the single-GPU mentioned in Appendix D.1, we needed to extract from our logs the effective number of training steps performed per trial.

In addition, we also considered the parallelization scheme applied during the tuning procedure. One issue with TabSyn was that we observed a general slowdown when the model was parallelized too heavily. This issue was even more marked on datasets with a large number of columns. We hence reduced the number trials per GPU and the global number of trials to 100 to fall back to a reasonable time for this model.

Finally, we measured cost on a typical configuration used during our tuning experiment: 8 Tesla V100-SXM2 32 GB. Considering those 8 GPUs, we used the following parallel allocation of trials: 64 for TVAE and CTGAN, 40 for TabDDPM, and 16 for TabSyn. A model that can be easily parallelized during the hyperparameter tuning phase offers a cost advantage. It is hence
Tuning costs estimation for the best models (continued).

<table><thead><tr><th>Dataset</th><th>Model</th><th>Emissions Training ↓</th><th>Energy Training ↓</th><th>Emissions Sampling ↓</th><th>Energy Sampling ↓</th></tr></thead><tbody><tr><td rowspan="6">Covertype</td><td>CTGAN</td><td>2.33±0.78 · 10<sup>-1</sup></td><td>3.46±1.15</td><td>1.92±0.27 · 10<sup>-5</sup></td><td>2.85±0.41 · 10<sup>-4</sup></td></tr><tr><td>TabDDPM</td><td>6.22±0.35 · 10<sup>-3</sup></td><td>9.23±0.53 · 10<sup>-2</sup></td><td>1.80±0.26 · 10<sup>-3</sup></td><td>2.67±0.38 · 10<sup>-2</sup></td></tr><tr><td>TabSyn</td><td>1.82±0.68 · 10<sup>-3</sup></td><td>1.26±0.72 · 10<sup>-2</sup></td><td>2.37±0.04 · 10<sup>-5</sup></td><td>3.52±0.06 · 10<sup>-4</sup></td></tr><tr><td>TVAE</td><td>1.04±0.81 · 10<sup>-1</sup></td><td>1.54±1.21</td><td>8.00±1.93 · 10<sup>-6</sup></td><td>1.19±0.29 · 10<sup>-4</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>4.52±0.02 · 10<sup>-4</sup></td><td>6.71±0.04 · 10<sup>-3</sup></td></tr><tr><td>UC-SMOTE</td><td>-</td><td>-</td><td>5.01±0.03 · 10<sup>-4</sup></td><td>7.43±0.04 · 10<sup>-3</sup></td></tr><tr><td rowspan="6">Diamonds</td><td>CTGAN</td><td>1.52±0.00 · 10<sup>-2</sup></td><td>2.26±0.01 · 10<sup>-1</sup></td><td>8.44±0.13 · 10<sup>-7</sup></td><td>1.25±0.02 · 10<sup>-5</sup></td></tr><tr><td>TabDDPM</td><td>3.33±0.71 · 10<sup>-4</sup></td><td>4.93±1.06 · 10<sup>-3</sup></td><td>1.30±0.47 · 10<sup>-4</sup></td><td>1.92±0.70 · 10<sup>-3</sup></td></tr><tr><td>TabSyn</td><td>1.21±0.18 · 10<sup>-3</sup></td><td>1.36±0.49 · 10<sup>-2</sup></td><td>1.67±0.89 · 10<sup>-5</sup></td><td>2.48±1.32 · 10<sup>-4</sup></td></tr><tr><td>TVAE</td><td>4.93±2.84 · 10<sup>-3</sup></td><td>7.31±4.21 · 10<sup>-2</sup></td><td>2.42±0.76 · 10<sup>-7</sup></td><td>3.59±1.12 · 10<sup>-6</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>1.32±0.01 · 10<sup>-5</sup></td><td>1.96±0.01 · 10<sup>-4</sup></td></tr><tr><td>UC-SMOTE</td><td>-</td><td>-</td><td>3.67±0.14 · 10<sup>-6</sup></td><td>5.44±0.21 · 10<sup>-5</sup></td></tr><tr><td rowspan="6">Heloc</td><td>CTGAN</td><td>1.93±1.51 · 10<sup>-2</sup></td><td>2.87±2.24 · 10<sup>-1</sup></td><td>6.03±4.19 · 10<sup>-7</sup></td><td>8.95±6.22 · 10<sup>-6</sup></td></tr><tr><td>TabDDPM</td><td>1.21±0.29 · 10<sup>-5</sup></td><td>1.80±0.43 · 10<sup>-4</sup></td><td>1.50±0.42 · 10<sup>-5</sup></td><td>2.23±0.63 · 10<sup>-4</sup></td></tr><tr><td>TabSyn</td><td>5.78±0.66 · 10<sup>-4</sup></td><td>6.91±0.18 · 10<sup>-3</sup></td><td>4.60±0.11 · 10<sup>-6</sup></td><td>6.83±0.16 · 10<sup>-5</sup></td></tr><tr><td>TVAE</td><td>1.88±1.11 · 10<sup>-3</sup></td><td>2.80±1.65 · 10<sup>-2</sup></td><td>1.15±0.43 · 10<sup>-7</sup></td><td>1.71±0.63 · 10<sup>-6</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>9.32±1.28 · 10<sup>-7</sup></td><td>1.38±0.19 · 10<sup>-5</sup></td></tr><tr><td>UC-SMOTE</td><td>-</td><td>-</td><td>2.02±0.07 · 10<sup>-6</sup></td><td>3.00±0.10 · 10<sup>-5</sup></td></tr><tr><td rowspan="6">Higgs</td><td>CTGAN</td><td>5.71±1.88 · 10<sup>-2</sup></td><td>8.47±2.79 · 10<sup>-1</sup></td><td>2.92±0.56 · 10<sup>-6</sup></td><td>4.33±0.84 · 10<sup>-5</sup></td></tr><tr><td>TabDDPM</td><td>4.01±0.25 · 10<sup>-4</sup></td><td>5.96±0.37 · 10<sup>-3</sup></td><td>1.77±0.18 · 10<sup>-4</sup></td><td>2.63±0.27 · 10<sup>-3</sup></td></tr><tr><td>TabSyn</td><td>2.88±1.12 · 10<sup>-3</sup></td><td>2.07±0.74 · 10<sup>-2</sup></td><td>3.20±1.72 · 10<sup>-5</sup></td><td>4.75±2.55 · 10<sup>-4</sup></td></tr><tr><td>TVAE</td><td>2.57±0.05 · 10<sup>-2</sup></td><td>3.81±0.08 · 10<sup>-1</sup></td><td>1.06±0.34 · 10<sup>-6</sup></td><td>1.58±0.51 · 10<sup>-5</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>2.01±0.19 · 10<sup>-6</sup></td><td>2.98±0.28 · 10<sup>-5</sup></td></tr><tr><td>UC-SMOTE</td><td>-</td><td>-</td><td>6.19±0.13 · 10<sup>-6</sup></td><td>9.18±0.20 · 10<sup>-5</sup></td></tr><tr><td rowspan="6">House 16h</td><td>CTGAN</td><td>4.42±2.48 · 10<sup>-3</sup></td><td>6.55±3.68 · 10<sup>-2</sup></td><td>1.24±0.16 · 10<sup>-7</sup></td><td>1.85±0.24 · 10<sup>-6</sup></td></tr><tr><td>TabDDPM</td><td>3.81±1.14 · 10<sup>-5</sup></td><td>5.66±1.69 · 10<sup>-4</sup></td><td>2.03±0.70 · 10<sup>-5</sup></td><td>3.01±1.04 · 10<sup>-4</sup></td></tr><tr><td>TabSyn</td><td>8.56±2.73 · 10<sup>-4</sup></td><td>9.40±1.12 · 10<sup>-3</sup></td><td>9.68±0.08 · 10<sup>-6</sup></td><td>1.44±0.01 · 10<sup>-4</sup></td></tr><tr><td>TVAE</td><td>4.12±0.02 · 10<sup>-3</sup></td><td>6.11±0.03 · 10<sup>-2</sup></td><td>1.40±0.17 · 10<sup>-7</sup></td><td>2.08±0.26 · 10<sup>-6</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>2.92±1.19 · 10<sup>-7</sup></td><td>4.34±1.77 · 10<sup>-6</sup></td></tr><tr><td>UC-SMOTE</td><td>-</td><td>-</td><td>4.04±0.48 · 10<sup>-7</sup></td><td>5.99±0.72 · 10<sup>-6</sup></td></tr><tr><td rowspan="6">Insurance</td><td>CTGAN</td><td>1.18±0.10 · 10<sup>-3</sup></td><td>1.75±0.15 · 10<sup>-2</sup></td><td>7.40±1.62 · 10<sup>-8</sup></td><td>1.10±0.24 · 10<sup>-6</sup></td></tr><tr><td>TabDDPM</td><td>2.83±0.29 · 10<sup>-6</sup></td><td>4.20±0.43 · 10<sup>-5</sup></td><td>2.65±0.94 · 10<sup>-5</sup></td><td>3.93±1.40 · 10<sup>-4</sup></td></tr><tr><td>TabSyn</td><td>3.45±0.04 · 10<sup>-4</sup></td><td>4.64±0.36 · 10<sup>-3</sup></td><td>5.87±2.03 · 10<sup>-7</sup></td><td>8.71±3.01 · 10<sup>-6</sup></td></tr><tr><td>TVAE</td><td>1.44±0.20 · 10<sup>-4</sup></td><td>2.14±0.29 · 10<sup>-3</sup></td><td>4.70±1.02 · 10<sup>-8</sup></td><td>6.98±1.51 · 10<sup>-7</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>1.83±0.26 · 10<sup>-7</sup></td><td>2.71±0.39 · 10<sup>-6</sup></td></tr><tr><td>UC-SMOTE</td><td>-</td><td>-</td><td>1.02±0.04 · 10<sup>-7</sup></td><td>1.51±0.06 · 10<sup>-6</sup></td></tr><tr><td rowspan="6">King</td><td>CTGAN</td><td>8.15±0.04 · 10<sup>-3</sup></td><td>1.21±0.01 · 10<sup>-1</sup></td><td>5.72±0.34 · 10<sup>-7</sup></td><td>8.49±0.50 · 10<sup>-6</sup></td></tr><tr><td>TabDDPM</td><td>9.27±0.56 · 10<sup>-5</sup></td><td>1.38±0.08 · 10<sup>-3</sup></td><td>5.08±0.49 · 10<sup>-5</sup></td><td>7.55±0.73 · 10<sup>-4</sup></td></tr><tr><td>TabSyn</td><td>9.40±1.26 · 10<sup>-4</sup></td><td>9.57±0.35 · 10<sup>-3</sup></td><td>9.15±0.02 · 10<sup>-6</sup></td><td>1.36±0.00 · 10<sup>-4</sup></td></tr><tr><td>TVAE</td><td>4.43±0.04 · 10<sup>-3</sup></td><td>6.57±0.07 · 10<sup>-2</sup></td><td>2.59±0.18 · 10<sup>-7</sup></td><td>3.85±0.26 · 10<sup>-6</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>8.77±0.84 · 10<sup>-6</sup></td><td>1.30±0.12 · 10<sup>-4</sup></td></tr><tr><td>UC-SMOTE</td><td>-</td><td>-</td><td>2.25±0.10 · 10<sup>-6</sup></td><td>3.34±0.14 · 10<sup>-5</sup></td></tr></tbody></table>
important to consider this aspect during the evaluation process. The results are presented in Table D.14.

<table><thead><tr><th rowspan="2">Dataset</th><th rowspan="2">Model</th><th colspan="3">Metrics</th></tr><tr><th>Energy<br>(kWh) ↓</th><th>Emissions<br>(Kg) ↓</th><th>Duration<br>(HH:MM) ↓</th></tr></thead><tbody><tr><td rowspan="6">Abalone</td><td>TVAE</td><td>0.00</td><td>0.01</td><td>00:02</td></tr><tr><td>CTGAN</td><td>0.01</td><td>0.08</td><td>00:19</td></tr><tr><td>TabDDPM</td><td>0.00</td><td>0.05</td><td>00:10</td></tr><tr><td>TabSyn</td><td>0.03</td><td>0.40</td><td>01:31</td></tr><tr><td>SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td>UC-SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td rowspan="6">Adult</td><td>TVAE</td><td>0.01</td><td>0.17</td><td>00:42</td></tr><tr><td>CTGAN</td><td>0.02</td><td>0.30</td><td>01:15</td></tr><tr><td>TabDDPM</td><td>0.01</td><td>0.12</td><td>00:25</td></tr><tr><td>TabSyn</td><td>0.08</td><td>0.91</td><td>03:27</td></tr><tr><td>SMOTE</td><td>0.00</td><td>0.01</td><td>00:04</td></tr><tr><td>UC-SMOTE</td><td>0.00</td><td>0.02</td><td>00:06</td></tr><tr><td rowspan="6">Bank<br>marketing</td><td>TVAE</td><td>0.01</td><td>0.10</td><td>00:25</td></tr><tr><td>CTGAN</td><td>0.03</td><td>0.38</td><td>01:35</td></tr><tr><td>TabDDPM</td><td>0.01</td><td>0.13</td><td>00:29</td></tr><tr><td>TabSyn</td><td>0.08</td><td>0.96</td><td>03:27</td></tr><tr><td>SMOTE</td><td>0.00</td><td>0.02</td><td>00:06</td></tr><tr><td>UC-SMOTE</td><td>0.00</td><td>0.02</td><td>00:05</td></tr><tr><td rowspan="6">Bike<br>sharing</td><td>TVAE</td><td>0.00</td><td>0.05</td><td>00:12</td></tr><tr><td>CTGAN</td><td>0.03</td><td>0.40</td><td>01:41</td></tr><tr><td>TabDDPM</td><td>0.01</td><td>0.12</td><td>00:22</td></tr><tr><td>TabSyn</td><td>0.05</td><td>0.61</td><td>02:18</td></tr><tr><td>SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td>UC-SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td rowspan="6">Black friday</td><td>TVAE</td><td>0.03</td><td>0.46</td><td>01:55</td></tr><tr><td>CTGAN</td><td>0.08</td><td>1.18</td><td>04:54</td></tr><tr><td>TabDDPM</td><td>0.01</td><td>0.13</td><td>00:23</td></tr><tr><td>TabSyn</td><td>0.21</td><td>2.40</td><td>09:19</td></tr><tr><td>SMOTE</td><td>0.00</td><td>0.06</td><td>00:19</td></tr><tr><td>UC-SMOTE</td><td>0.01</td><td>0.22</td><td>01:07</td></tr><tr><td rowspan="6">Cardio</td><td>TVAE</td><td>0.01</td><td>0.16</td><td>00:41</td></tr><tr><td>CTGAN</td><td>0.03</td><td>0.51</td><td>02:07</td></tr><tr><td>TabDDPM</td><td>0.01</td><td>0.08</td><td>00:12</td></tr><tr><td>TabSyn</td><td>0.10</td><td>1.38</td><td>04:13</td></tr><tr><td>SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td>UC-SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td rowspan="6">Churn</td><td>TVAE</td><td>0.00</td><td>0.03</td><td>00:07</td></tr><tr><td>CTGAN</td><td>0.02</td><td>0.29</td><td>01:11</td></tr><tr><td>TabDDPM</td><td>0.02</td><td>0.31</td><td>00:48</td></tr><tr><td>TabSyn</td><td>0.04</td><td>0.53</td><td>02:02</td></tr><tr><td>SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td>UC-SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr></tbody></table>
Tuning costs estimation for the best models (continued).

<table><caption>**Table D.13:** CO₂ emissions (in Kg) and Energy Consumption (in kWh) of the benchmark challengers. The energy consumption is obtained by summing the CPU, GPU and RAM energy. Training costs are given for all models on the same basis of 400 epochs. Sampling costs are given for 5 samples. The best values are formatted in **bold green** and the worse are in **red**.</caption><thead><tr><th>Dataset</th><th>Model</th><th>Emissions Training ↓</th><th>Energy Training ↓</th><th>Emissions Sampling ↓</th><th>Energy Sampling ↓</th></tr></thead><tbody><tr><td rowspan="6">Minibootne</td><td>CTGAN</td><td>3.16±1.09 · 10<sup>-2</sup></td><td>4.69±1.62 · 10<sup>-1</sup></td><td>3.50±0.24 · 10<sup>-6</sup></td><td>5.20±0.35 · 10<sup>-5</sup></td></tr><tr><td>TabDDPM</td><td>4.50±1.33 · 10<sup>-4</sup></td><td>6.68±1.97 · 10<sup>-3</sup></td><td>1.84±0.69 · 10<sup>-4</sup></td><td>2.74±1.03 · 10<sup>-3</sup></td></tr><tr><td>TabSyn</td><td>3.41±0.61 · 10<sup>-3</sup></td><td>3.18±0.79 · 10<sup>-2</sup></td><td>5.57±0.07 · 10<sup>-5</sup></td><td>8.26±0.11 · 10<sup>-4</sup></td></tr><tr><td>TVAE</td><td>2.18±2.12 · 10<sup>-2</sup></td><td>3.24±3.14 · 10<sup>-1</sup></td><td>1.94±0.22 · 10<sup>-6</sup></td><td>2.88±0.32 · 10<sup>-5</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>4.39±0.34 · 10<sup>-6</sup></td><td>6.51±0.51 · 10<sup>-5</sup></td></tr><tr><td>UC-SMOTE</td><td>-</td><td>-</td><td>1.32±0.01 · 10<sup>-5</sup></td><td>1.95±0.02 · 10<sup>-4</sup></td></tr><tr><td rowspan="6">Moons</td><td>CTGAN</td><td>1.15±0.43 · 10<sup>-2</sup></td><td>1.71±0.64 · 10<sup>-1</sup></td><td>5.02±1.07 · 10<sup>-7</sup></td><td>7.45±1.59 · 10<sup>-6</sup></td></tr><tr><td>TabDDPM</td><td>1.31±0.77 · 10<sup>-4</sup></td><td>1.94±1.14 · 10<sup>-3</sup></td><td>7.39±5.33 · 10<sup>-5</sup></td><td>1.10±0.79 · 10<sup>-3</sup></td></tr><tr><td>TabSyn</td><td>9.26±2.41 · 10<sup>-4</sup></td><td>1.14±0.36 · 10<sup>-2</sup></td><td>1.22±0.65 · 10<sup>-5</sup></td><td>1.81±0.96 · 10<sup>-4</sup></td></tr><tr><td>TVAE</td><td>3.37±0.24 · 10<sup>-3</sup></td><td>5.00±0.36 · 10<sup>-2</sup></td><td>1.78±0.43 · 10<sup>-7</sup></td><td>2.65±0.64 · 10<sup>-6</sup></td></tr><tr><td>SMOTE</td><td>-</td><td>-</td><td>2.44±0.52 · 10<sup>-7</sup></td><td>3.63±0.78 · 10<sup>-6</sup></td></tr><tr><td>UC-SMOTE</td><td>-</td><td>-</td><td>1.03±0.12 · 10<sup>-6</sup></td><td>1.53±0.18 · 10<sup>-5</sup></td></tr></tbody></table>

## Appendix D.2. Whole Tuning Cost Estimation

As mentioned in Section 3.2 we could not perform the hyperparameter search and training phases on a uniform hardware and software architecture and we estimated the tuning cost with Equation (1).

Each trial can be stopped based on three conditions: an early stopping decided by the model, a poor C2ST performance or a time limit. Therefore, to get an accurate estimate of the init-cost and the cost-per-step from the single-GPU mentioned in Appendix D.1, we needed to extract from our logs the effective number of training steps performed per trial.

In addition, we also considered the parallelization scheme applied during the tuning procedure. One issue with TabSyn was that we observed a general slowdown when the model was parallelized too heavily. This issue was even more marked on datasets with a large number of columns. We hence reduced the number trials per GPU and the global number of trials to 100 to fall back to a reasonable time for this model.

Finally, we measured cost on a typical configuration used during our tuning experiment: 8 Tesla V100-SXM2 32 GB. Considering those 8 GPUs, we used the following parallel allocation of trials: 64 for TVAE and CTGAN, 40 for TabDDPM, and 16 for TabSyn. A model that can be easily parallelized during the hyperparameter tuning phase offers a cost advantage. It is hence
Tuning costs estimation (continued).

<table><thead><tr><th rowspan="2">Dataset</th><th rowspan="2">Model</th><th colspan="3">Metrics</th></tr><tr><th>Energy<br>(kWh) ↓</th><th>Emissions<br>(Kg) ↓</th><th>Duration<br>(HH:MM) ↓</th></tr></thead><tbody><tr><td rowspan="5">Covertype</td><td>TVAE</td><td>0.19</td><td>2.77</td><td>11:34</td></tr><tr><td>CTGAN</td><td>0.54</td><td>8.04</td><td>33:17</td></tr><tr><td>TabDDPM</td><td>0.03</td><td>0.49</td><td>01:48</td></tr><tr><td>TabSyn</td><td>0.19</td><td>1.53</td><td>07:54</td></tr><tr><td>SMOTE</td><td>0.02</td><td>0.26</td><td>01:19</td></tr><tr><td rowspan="5">Diamonds</td><td>UC-SMOTE</td><td>0.02</td><td>0.28</td><td>01:27</td></tr><tr><td>TVAE</td><td>0.01</td><td>0.10</td><td>00:25</td></tr><tr><td>CTGAN</td><td>0.03</td><td>0.40</td><td>01:39</td></tr><tr><td>TabDDPM</td><td>0.01</td><td>0.15</td><td>00:24</td></tr><tr><td>TabSyn</td><td>0.08</td><td>1.01</td><td>03:22</td></tr><tr><td rowspan="5">Heloc</td><td>SMOTE</td><td>0.00</td><td>0.01</td><td>00:02</td></tr><tr><td>UC-SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td>TVAE</td><td>0.00</td><td>0.04</td><td>00:10</td></tr><tr><td>CTGAN</td><td>0.03</td><td>0.49</td><td>02:02</td></tr><tr><td>TabDDPM</td><td>0.00</td><td>0.03</td><td>00:05</td></tr><tr><td rowspan="5">Higgs</td><td>SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td>UC-SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td>TVAE</td><td>0.04</td><td>0.53</td><td>02:13</td></tr><tr><td>CTGAN</td><td>0.11</td><td>1.61</td><td>06:42</td></tr><tr><td>TabDDPM</td><td>0.01</td><td>0.10</td><td>00:15</td></tr><tr><td rowspan="5">House<br>16h</td><td>SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td>UC-SMOTE</td><td>0.00</td><td>0.00</td><td>00:01</td></tr><tr><td>TVAE</td><td>0.01</td><td>0.09</td><td>00:23</td></tr><tr><td>CTGAN</td><td>0.01</td><td>0.10</td><td>00:25</td></tr><tr><td>TabDDPM</td><td>0.00</td><td>0.04</td><td>00:06</td></tr><tr><td rowspan="5">Insurance</td><td>SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td>UC-SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td>TVAE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td>CTGAN</td><td>0.00</td><td>0.03</td><td>00:06</td></tr><tr><td>TabDDPM</td><td>0.00</td><td>0.05</td><td>00:12</td></tr><tr><td rowspan="5">King</td><td>SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td>UC-SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td>TVAE</td><td>0.01</td><td>0.09</td><td>00:23</td></tr><tr><td>CTGAN</td><td>0.01</td><td>0.21</td><td>00:51</td></tr><tr><td>TabDDPM</td><td>0.01</td><td>0.17</td><td>00:27</td></tr><tr><td rowspan="5">Insurance</td><td>SMOTE</td><td>0.00</td><td>0.00</td><td>00:01</td></tr><tr><td>UC-SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr></tbody></table>
important to consider this aspect during the evaluation process. The results are presented in Table D.14.

<table><thead><tr><th rowspan="2">Dataset</th><th rowspan="2">Model</th><th colspan="3">Metrics</th></tr><tr><th>Energy<br>(kWh) ↓</th><th>Emissions<br>(Kg) ↓</th><th>Duration<br>(HH:MM) ↓</th></tr></thead><tbody><tr><td rowspan="6">Abalone</td><td>TVAE</td><td>0.00</td><td>0.01</td><td>00:02</td></tr><tr><td>CTGAN</td><td>0.01</td><td>0.08</td><td>00:19</td></tr><tr><td>TabDDPM</td><td>0.00</td><td>0.05</td><td>00:10</td></tr><tr><td>TabSyn</td><td>0.03</td><td>0.40</td><td>01:31</td></tr><tr><td>SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td>UC-SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td rowspan="6">Adult</td><td>TVAE</td><td>0.01</td><td>0.17</td><td>00:42</td></tr><tr><td>CTGAN</td><td>0.02</td><td>0.30</td><td>01:15</td></tr><tr><td>TabDDPM</td><td>0.01</td><td>0.12</td><td>00:25</td></tr><tr><td>TabSyn</td><td>0.08</td><td>0.91</td><td>03:27</td></tr><tr><td>SMOTE</td><td>0.00</td><td>0.01</td><td>00:04</td></tr><tr><td>UC-SMOTE</td><td>0.00</td><td>0.02</td><td>00:06</td></tr><tr><td rowspan="6">Bank<br>marketing</td><td>TVAE</td><td>0.01</td><td>0.10</td><td>00:25</td></tr><tr><td>CTGAN</td><td>0.03</td><td>0.38</td><td>01:35</td></tr><tr><td>TabDDPM</td><td>0.01</td><td>0.13</td><td>00:29</td></tr><tr><td>TabSyn</td><td>0.08</td><td>0.96</td><td>03:27</td></tr><tr><td>SMOTE</td><td>0.00</td><td>0.02</td><td>00:06</td></tr><tr><td>UC-SMOTE</td><td>0.00</td><td>0.02</td><td>00:05</td></tr><tr><td rowspan="6">Bike<br>sharing</td><td>TVAE</td><td>0.00</td><td>0.05</td><td>00:12</td></tr><tr><td>CTGAN</td><td>0.03</td><td>0.40</td><td>01:41</td></tr><tr><td>TabDDPM</td><td>0.01</td><td>0.12</td><td>00:22</td></tr><tr><td>TabSyn</td><td>0.05</td><td>0.61</td><td>02:18</td></tr><tr><td>SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td>UC-SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td rowspan="6">Black<br>friday</td><td>TVAE</td><td>0.03</td><td>0.46</td><td>01:55</td></tr><tr><td>CTGAN</td><td>0.08</td><td>1.18</td><td>04:54</td></tr><tr><td>TabDDPM</td><td>0.01</td><td>0.13</td><td>00:23</td></tr><tr><td>TabSyn</td><td>0.21</td><td>2.40</td><td>09:19</td></tr><tr><td>SMOTE</td><td>0.00</td><td>0.06</td><td>00:19</td></tr><tr><td>UC-SMOTE</td><td>0.01</td><td>0.22</td><td>01:07</td></tr><tr><td rowspan="6">Cardio</td><td>TVAE</td><td>0.01</td><td>0.16</td><td>00:41</td></tr><tr><td>CTGAN</td><td>0.03</td><td>0.51</td><td>02:07</td></tr><tr><td>TabDDPM</td><td>0.01</td><td>0.08</td><td>00:12</td></tr><tr><td>TabSyn</td><td>0.10</td><td>1.38</td><td>04:13</td></tr><tr><td>SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td>UC-SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td rowspan="6">Churn</td><td>TVAE</td><td>0.00</td><td>0.03</td><td>00:07</td></tr><tr><td>CTGAN</td><td>0.02</td><td>0.29</td><td>01:11</td></tr><tr><td>TabDDPM</td><td>0.02</td><td>0.31</td><td>00:48</td></tr><tr><td>TabSyn</td><td>0.04</td><td>0.53</td><td>02:02</td></tr><tr><td>SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td>UC-SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr></tbody></table>
Tuning costs estimation (continued).

<table><caption>**Table D.14:** Estimated hyperparameter search cost based on the estimated training cost of the best models presented in Table D.13. All costs associated with TabSyn include those incurred by the VAE and the denoiser. The energy and emissions values are rounded to two decimals and take into account the number of trials we could run in parallel per model. The best values per metric are formatted in **bold green** and the worse are in **red**.</caption><thead><tr><th rowspan="2">Dataset</th><th rowspan="2">Model</th><th colspan="3">Metrics</th></tr><tr><th>Energy<br>(kWh) ↓</th><th>Emissions<br>(Kg) ↓</th><th>Duration<br>(HH:MM) ↓</th></tr></thead><tbody><tr><td rowspan="6">Miniboo<br>ne</td><td>TVAE</td><td>0.04</td><td>0.56</td><td>02:19</td></tr><tr><td>CTGAN</td><td>0.05</td><td>0.73</td><td>02:59</td></tr><tr><td>TabDDPM</td><td>0.01</td><td>0.10</td><td>00:14</td></tr><tr><td>TabSyn</td><td>0.31</td><td>2.02</td><td>11:44</td></tr><tr><td>SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td>UC-SMOTE</td><td>0.00</td><td>0.01</td><td>00:02</td></tr><tr><td rowspan="6">Moons</td><td>TVAE</td><td>0.01</td><td>0.08</td><td>00:20</td></tr><tr><td>CTGAN</td><td>0.02</td><td>0.29</td><td>01:12</td></tr><tr><td>TabDDPM</td><td>0.01</td><td>0.08</td><td>00:12</td></tr><tr><td>TabSyn</td><td>0.05</td><td>0.87</td><td>02:35</td></tr><tr><td>SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td>UC-SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr></tbody></table>

## Appendix E. Base Models and their Tuned Versions

We also trained the models using their native codes and hyperparameters to provide an additional reference for comparison with their tuned versions. Table E.15 presents the results as evaluated under the same procedure as the tuned models for C2ST, DCR-Rate, ML-Efficacy, column-wise similarity (named "Shape"), and pair-wise correlation (named "Pair"). For TabDDPM, since there is no default hyperparameters provided [8], we fixed one based on the base configuration provided in the authors' GitHub repository.

<table><thead><tr><th rowspan="2">Dataset</th><th rowspan="2">Model</th><th colspan="5">Metrics</th></tr><tr><th>C2ST ↓</th><th>DCR-Rate ↓</th><th>ML-Efficacy ↑</th><th>Shape ↑</th><th>Pair ↑</th></tr></thead><tbody><tr><td rowspan="6">Abalone</td><td>Train Copy</td><td>0.51 ± 0.00</td><td>1.00 ± 0.00</td><td>0.23 ± 0.01</td><td>0.96 ± 0.01</td><td>0.88 ± 0.01</td></tr><tr><td>CTGAN</td><td>0.99 ± 0.01</td><td>0.60 ± 0.01</td><td>0.12 ± 0.03</td><td>0.87 ± 0.02</td><td>0.76 ± 0.01</td></tr><tr><td>TVAE</td><td>0.96 ± 0.00</td><td>0.61 ± 0.02</td><td>0.22 ± 0.02</td><td>0.91 ± 0.02</td><td>0.83 ± 0.03</td></tr><tr><td>TabDDPM</td><td>1.00 ± 0.00</td><td>0.64 ± 0.01</td><td>0.00 ± 0.00</td><td>0.85 ± 0.01</td><td>0.70 ± 0.01</td></tr><tr><td>TabSyn</td><td>0.78 ± 0.02</td><td>0.64 ± 0.01</td><td>0.22 ± 0.01</td><td>0.95 ± 0.01</td><td>0.88 ± 0.01</td></tr><tr><td rowspan="4">Adult</td><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.71 ± 0.01</td><td>0.99 ± 0.00</td><td>0.98 ± 0.00</td></tr><tr><td>CTGAN</td><td>0.96 ± 0.01</td><td>0.61 ± 0.01</td><td>0.61 ± 0.05</td><td>0.88 ± 0.02</td><td>0.82 ± 0.02</td></tr><tr><td>TVAE</td><td>0.94 ± 0.01</td><td>0.61 ± 0.00</td><td>0.63 ± 0.03</td><td>0.92 ± 0.00</td><td>0.85 ± 0.01</td></tr><tr><td>TabDDPM</td><td>0.66 ± 0.01</td><td>0.62 ± 0.00</td><td>0.67 ± 0.00</td><td>0.98 ± 0.00</td><td>0.95 ± 0.00</td></tr></tbody></table>
Tuning costs estimation (continued).

<table><thead><tr><th rowspan="2">Dataset</th><th rowspan="2">Model</th><th colspan="3">Metrics</th></tr><tr><th>Energy<br>(kWh) ↓</th><th>Emissions<br>(Kg) ↓</th><th>Duration<br>(HH:MM) ↓</th></tr></thead><tbody><tr><td rowspan="5">Covertype</td><td>TVAE</td><td>0.19</td><td>2.77</td><td>11:34</td></tr><tr><td>CTGAN</td><td>0.54</td><td>8.04</td><td>33:17</td></tr><tr><td>TabDDPM</td><td>0.03</td><td>0.49</td><td>01:48</td></tr><tr><td>TabSyn</td><td>0.19</td><td>1.53</td><td>07:54</td></tr><tr><td>SMOTE</td><td>0.02</td><td>0.26</td><td>01:19</td></tr><tr><td rowspan="5">Diamonds</td><td>UC-SMOTE</td><td>0.02</td><td>0.28</td><td>01:27</td></tr><tr><td>TVAE</td><td>0.01</td><td>0.10</td><td>00:25</td></tr><tr><td>CTGAN</td><td>0.03</td><td>0.40</td><td>01:39</td></tr><tr><td>TabDDPM</td><td>0.01</td><td>0.15</td><td>00:24</td></tr><tr><td>TabSyn</td><td>0.08</td><td>1.01</td><td>03:22</td></tr><tr><td rowspan="5">Heloc</td><td>SMOTE</td><td>0.00</td><td>0.01</td><td>00:02</td></tr><tr><td>UC-SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td>TVAE</td><td>0.00</td><td>0.04</td><td>00:10</td></tr><tr><td>CTGAN</td><td>0.03</td><td>0.49</td><td>02:02</td></tr><tr><td>TabDDPM</td><td>0.00</td><td>0.03</td><td>00:05</td></tr><tr><td rowspan="5">Higgs</td><td>TabSyn</td><td>0.04</td><td>0.54</td><td>02:08</td></tr><tr><td>SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td>UC-SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td>TVAE</td><td>0.04</td><td>0.53</td><td>02:13</td></tr><tr><td>CTGAN</td><td>0.11</td><td>1.61</td><td>06:42</td></tr><tr><td rowspan="5">House<br>16h</td><td>TabDDPM</td><td>0.01</td><td>0.10</td><td>00:15</td></tr><tr><td>TabSyn</td><td>0.18</td><td>1.58</td><td>07:50</td></tr><tr><td>SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td>UC-SMOTE</td><td>0.00</td><td>0.00</td><td>00:01</td></tr><tr><td>TVAE</td><td>0.01</td><td>0.09</td><td>00:23</td></tr><tr><td rowspan="5">Insurance</td><td>CTGAN</td><td>0.01</td><td>0.10</td><td>00:25</td></tr><tr><td>TabDDPM</td><td>0.00</td><td>0.04</td><td>00:06</td></tr><tr><td>TabSyn</td><td>0.05</td><td>0.58</td><td>02:16</td></tr><tr><td>SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td>UC-SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td rowspan="5">King</td><td>TVAE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td>CTGAN</td><td>0.00</td><td>0.03</td><td>00:06</td></tr><tr><td>TabDDPM</td><td>0.00</td><td>0.05</td><td>00:12</td></tr><tr><td>TabSyn</td><td>0.03</td><td>0.35</td><td>01:25</td></tr><tr><td>SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td>TVAE</td><td>0.01</td><td>0.09</td><td>00:23</td></tr><tr><td rowspan="5">Insurance</td><td>CTGAN</td><td>0.01</td><td>0.21</td><td>00:51</td></tr><tr><td>TabDDPM</td><td>0.01</td><td>0.17</td><td>00:27</td></tr><tr><td>TabSyn</td><td>0.05</td><td>0.66</td><td>02:26</td></tr><tr><td>SMOTE</td><td>0.00</td><td>0.00</td><td>00:01</td></tr><tr><td>UC-SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr></tbody></table>
Results per datasets and models under diverse metrics for the base models (continued).

<table><thead><tr><th rowspan="2">Dataset</th><th rowspan="2">Model</th><th colspan="5">Metrics</th></tr><tr><th>C2ST ↓</th><th>DCR-Rate ↓</th><th>ML-Efficacy ↑</th><th>Shape ↑</th><th>Pair ↑</th></tr></thead><tbody><tr><td rowspan="5">Bank marketing</td><td>TabSyn</td><td>0.71 ± 0.06</td><td>0.62 ± 0.00</td><td>0.66 ± 0.01</td><td>0.98 ± 0.01</td><td>0.95 ± 0.02</td></tr><tr><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.54 ± 0.01</td><td>0.99 ± 0.00</td><td>0.98 ± 0.01</td></tr><tr><td>CTGAN</td><td>0.89 ± 0.01</td><td>0.62 ± 0.01</td><td>0.33 ± 0.05</td><td>0.92 ± 0.00</td><td>0.86 ± 0.01</td></tr><tr><td>TVAE</td><td>0.95 ± 0.00</td><td>0.62 ± 0.00</td><td>0.52 ± 0.02</td><td>0.91 ± 0.01</td><td>0.84 ± 0.02</td></tr><tr><td>TabDDPM</td><td>0.68 ± 0.01</td><td>0.63 ± 0.01</td><td>0.48 ± 0.02</td><td>0.99 ± 0.01</td><td>0.96 ± 0.00</td></tr><tr><td rowspan="5">Bike sharing</td><td>TabSyn</td><td>0.65 ± 0.04</td><td>0.63 ± 0.01</td><td>0.47 ± 0.01</td><td>0.98 ± 0.01</td><td>0.96 ± 0.00</td></tr><tr><td>Train Copy</td><td>0.50 ± 0.01</td><td>1.00 ± 0.00</td><td>0.94 ± 0.00</td><td>0.99 ± 0.00</td><td>0.53 ± 0.00</td></tr><tr><td>CTGAN</td><td>1.00 ± 0.00</td><td>0.61 ± 0.00</td><td>0.37 ± 0.03</td><td>0.93 ± 0.01</td><td>0.51 ± 0.01</td></tr><tr><td>TVAE</td><td>1.00 ± 0.00</td><td>0.61 ± 0.01</td><td>0.42 ± 0.08</td><td>0.91 ± 0.01</td><td>0.51 ± 0.01</td></tr><tr><td>TabDDPM</td><td>0.85 ± 0.01</td><td>0.61 ± 0.00</td><td>0.67 ± 0.03</td><td>0.98 ± 0.00</td><td>0.53 ± 0.00</td></tr><tr><td rowspan="5">Black friday</td><td>TabSyn</td><td>0.94 ± 0.03</td><td>0.61 ± 0.00</td><td>0.31 ± 0.04</td><td>0.95 ± 0.01</td><td>0.52 ± 0.01</td></tr><tr><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.53 ± 0.01</td><td>1.00 ± 0.00</td><td>0.99 ± 0.00</td></tr><tr><td>CTGAN</td><td>0.92 ± 0.01</td><td>0.66 ± 0.01</td><td>0.40 ± 0.01</td><td>0.94 ± 0.01</td><td>0.84 ± 0.01</td></tr><tr><td>TVAE</td><td>0.98 ± 0.00</td><td>0.67 ± 0.01</td><td>0.29 ± 0.08</td><td>0.83 ± 0.01</td><td>0.73 ± 0.01</td></tr><tr><td>TabDDPM</td><td>0.92 ± 0.00</td><td>0.67 ± 0.01</td><td>0.31 ± 0.03</td><td>0.99 ± 0.00</td><td>0.98 ± 0.00</td></tr><tr><td rowspan="5">Cardio</td><td>TabSyn</td><td>0.91 ± 0.01</td><td>0.68 ± 0.00</td><td>0.13 ± 0.03</td><td>0.98 ± 0.00</td><td>0.96 ± 0.01</td></tr><tr><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.72 ± 0.01</td><td>1.00 ± 0.00</td><td>0.98 ± 0.01</td></tr><tr><td>CTGAN</td><td>1.00 ± 0.01</td><td>0.62 ± 0.01</td><td>0.67 ± 0.02</td><td>0.93 ± 0.01</td><td>0.93 ± 0.01</td></tr><tr><td>TVAE</td><td>1.00 ± 0.00</td><td>0.63 ± 0.00</td><td>0.67 ± 0.04</td><td>0.88 ± 0.01</td><td>0.90 ± 0.02</td></tr><tr><td>TabDDPM</td><td>0.59 ± 0.00</td><td>0.64 ± 0.00</td><td>0.72 ± 0.01</td><td>0.99 ± 0.00</td><td>0.96 ± 0.02</td></tr><tr><td rowspan="5">Churn</td><td>TabSyn</td><td>0.58 ± 0.01</td><td>0.64 ± 0.01</td><td>0.72 ± 0.01</td><td>0.99 ± 0.01</td><td>0.97 ± 0.01</td></tr><tr><td>Train Copy</td><td>0.50 ± 0.01</td><td>1.00 ± 0.00</td><td>0.59 ± 0.02</td><td>0.95 ± 0.00</td><td>0.87 ± 0.01</td></tr><tr><td>CTGAN</td><td>0.87 ± 0.02</td><td>0.60 ± 0.00</td><td>0.19 ± 0.10</td><td>0.85 ± 0.02</td><td>0.79 ± 0.00</td></tr><tr><td>TVAE</td><td>0.98 ± 0.01</td><td>0.60 ± 0.01</td><td>0.45 ± 0.10</td><td>0.75 ± 0.03</td><td>0.63 ± 0.03</td></tr><tr><td>TabDDPM</td><td>1.00 ± 0.00</td><td>0.65 ± 0.40</td><td>0.00 ± 0.00</td><td>0.59 ± 0.02</td><td>0.56 ± 0.02</td></tr><tr><td rowspan="5">Covertype</td><td>TabSyn</td><td>0.64 ± 0.03</td><td>0.61 ± 0.01</td><td>0.43 ± 0.13</td><td>0.92 ± 0.01</td><td>0.85 ± 0.00</td></tr><tr><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.90 ± 0.00</td><td>1.00 ± 0.00</td><td>1.00 ± 0.01</td></tr><tr><td>CTGAN</td><td>1.00 ± 0.00</td><td>0.60 ± 0.00</td><td>0.66 ± 0.01</td><td>0.97 ± 0.00</td><td>0.94 ± 0.01</td></tr><tr><td>TVAE</td><td>1.00 ± 0.00</td><td>0.60 ± 0.00</td><td>0.72 ± 0.01</td><td>0.98 ± 0.00</td><td>0.95 ± 0.01</td></tr><tr><td>TabDDPM</td><td>0.82 ± 0.01</td><td>0.60 ± 0.00</td><td>0.73 ± 0.01</td><td>1.00 ± 0.00</td><td>0.99 ± 0.00</td></tr><tr><td rowspan="5">Diamonds</td><td>TabSyn</td><td>0.72 ± 0.04</td><td>0.60 ± 0.00</td><td>0.79 ± 0.03</td><td>0.99 ± 0.00</td><td>0.99 ± 0.00</td></tr><tr><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.98 ± 0.00</td><td>0.99 ± 0.00</td><td>0.77 ± 0.01</td></tr><tr><td>CTGAN</td><td>0.98 ± 0.00</td><td>0.60 ± 0.00</td><td>0.87 ± 0.01</td><td>0.91 ± 0.01</td><td>0.75 ± 0.04</td></tr><tr><td>TVAE</td><td>0.97 ± 0.01</td><td>0.60 ± 0.01</td><td>0.91 ± 0.01</td><td>0.92 ± 0.02</td><td>0.76 ± 0.03</td></tr><tr><td>TabDDPM</td><td>0.76 ± 0.01</td><td>0.61 ± 0.00</td><td>0.97 ± 0.00</td><td>0.99 ± 0.01</td><td>0.71 ± 0.01</td></tr><tr><td rowspan="5">Heloc</td><td>TabSyn</td><td>0.95 ± 0.02</td><td>0.64 ± 0.00</td><td>0.19 ± 0.06</td><td>0.96 ± 0.00</td><td>0.72 ± 0.01</td></tr><tr><td>Train Copy</td><td>0.50 ± 0.01</td><td>1.00 ± 0.00</td><td>0.70 ± 0.01</td><td>0.99 ± 0.00</td><td>0.97 ± 0.01</td></tr><tr><td>CTGAN</td><td>1.00 ± 0.00</td><td>0.63 ± 0.00</td><td>0.40 ± 0.14</td><td>0.87 ± 0.05</td><td>0.87 ± 0.07</td></tr><tr><td>TVAE</td><td>0.98 ± 0.01</td><td>0.63 ± 0.02</td><td>0.69 ± 0.01</td><td>0.90 ± 0.00</td><td>0.75 ± 0.01</td></tr><tr><td>TabDDPM</td><td>0.71 ± 0.01</td><td>0.64 ± 0.02</td><td>0.70 ± 0.01</td><td>0.97 ± 0.00</td><td>0.94 ± 0.01</td></tr><tr><td rowspan="5">Higgs</td><td>TabSyn</td><td>0.75 ± 0.01</td><td>0.65 ± 0.01</td><td>0.69 ± 0.01</td><td>0.97 ± 0.00</td><td>0.96 ± 0.01</td></tr><tr><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.74 ± 0.00</td><td>0.99 ± 0.00</td><td>0.99 ± 0.00</td></tr><tr><td>CTGAN</td><td>1.00 ± 0.00</td><td>0.60 ± 0.00</td><td>0.61 ± 0.08</td><td>0.87 ± 0.02</td><td>0.95 ± 0.00</td></tr><tr><td>TVAE</td><td>1.00 ± 0.00</td><td>0.61 ± 0.02</td><td>0.68 ± 0.02</td><td>0.78 ± 0.00</td><td>0.94 ± 0.01</td></tr><tr><td>TabDDPM</td><td>0.79 ± 0.02</td><td>0.60 ± 0.01</td><td>0.72 ± 0.01</td><td>0.98 ± 0.01</td><td>0.93 ± 0.02</td></tr><tr><td></td><td>TabSyn</td><td>0.59 ± 0.01</td><td>0.61 ± 0.00</td><td>0.73 ± 0.00</td><td>0.94 ± 0.00</td><td>0.99 ± 0.00</td></tr></tbody></table>
Tuning costs estimation (continued).

<table><caption>**Table D.14:** Estimated hyperparameter search cost based on the estimated training cost of the best models presented in Table D.13. All costs associated with TabSyn include those incurred by the VAE and the denoiser. The energy and emissions values are rounded to two decimals and take into account the number of trials we could run in parallel per model. The best values per metric are formatted in **bold green** and the worse are in **red**.</caption><thead><tr><th rowspan="2">Dataset</th><th rowspan="2">Model</th><th colspan="3">Metrics</th></tr><tr><th>Energy<br>(kWh) ↓</th><th>Emissions<br>(Kg) ↓</th><th>Duration<br>(HH:MM) ↓</th></tr></thead><tbody><tr><td rowspan="6">Miniboo<br>ne</td><td>TVAE</td><td>0.04</td><td>0.56</td><td>02:19</td></tr><tr><td>CTGAN</td><td>0.05</td><td>0.73</td><td>02:59</td></tr><tr><td>TabDDPM</td><td>0.01</td><td>0.10</td><td>00:14</td></tr><tr><td>TabSyn</td><td>0.31</td><td>2.02</td><td>11:44</td></tr><tr><td>SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td>UC-SMOTE</td><td>0.00</td><td>0.01</td><td>00:02</td></tr><tr><td rowspan="6">Moons</td><td>TVAE</td><td>0.01</td><td>0.08</td><td>00:20</td></tr><tr><td>CTGAN</td><td>0.02</td><td>0.29</td><td>01:12</td></tr><tr><td>TabDDPM</td><td>0.01</td><td>0.08</td><td>00:12</td></tr><tr><td>TabSyn</td><td>0.05</td><td>0.87</td><td>02:35</td></tr><tr><td>SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr><tr><td>UC-SMOTE</td><td>0.00</td><td>0.00</td><td>00:00</td></tr></tbody></table>

## Appendix E. Base Models and their Tuned Versions

We also trained the models using their native codes and hyperparameters to provide an additional reference for comparison with their tuned versions. Table E.15 presents the results as evaluated under the same procedure as the tuned models for C2ST, DCR-Rate, ML-Efficacy, column-wise similarity (named "Shape"), and pair-wise correlation (named "Pair"). For TabDDPM, since there is no default hyperparameters provided [14], we fixed one based on the base configuration provided in the authors' GitHub repository.

<table><thead><tr><th rowspan="2">Dataset</th><th rowspan="2">Model</th><th colspan="5">Metrics</th></tr><tr><th>C2ST ↓</th><th>DCR-Rate ↓</th><th>ML-Efficacy ↑</th><th>Shape ↑</th><th>Pair ↑</th></tr></thead><tbody><tr><td rowspan="6">Abalone</td><td>Train Copy</td><td>0.51 ± 0.00</td><td>1.00 ± 0.00</td><td>0.23 ± 0.01</td><td>0.96 ± 0.01</td><td>0.88 ± 0.01</td></tr><tr><td>CTGAN</td><td>0.99 ± 0.01</td><td>0.60 ± 0.01</td><td>0.12 ± 0.03</td><td>0.87 ± 0.02</td><td>0.76 ± 0.01</td></tr><tr><td>TVAE</td><td>0.96 ± 0.00</td><td>0.61 ± 0.02</td><td>0.22 ± 0.02</td><td>0.91 ± 0.02</td><td>0.83 ± 0.03</td></tr><tr><td>TabDDPM</td><td>1.00 ± 0.00</td><td>0.64 ± 0.01</td><td>0.00 ± 0.00</td><td>0.85 ± 0.01</td><td>0.70 ± 0.01</td></tr><tr><td>TabSyn</td><td>0.78 ± 0.02</td><td>0.64 ± 0.01</td><td>0.22 ± 0.01</td><td>0.95 ± 0.01</td><td>0.88 ± 0.01</td></tr><tr><td rowspan="4">Adult</td><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.71 ± 0.01</td><td>0.99 ± 0.00</td><td>0.98 ± 0.00</td></tr><tr><td>CTGAN</td><td>0.96 ± 0.01</td><td>0.61 ± 0.01</td><td>0.61 ± 0.05</td><td>0.88 ± 0.02</td><td>0.82 ± 0.02</td></tr><tr><td>TVAE</td><td>0.94 ± 0.01</td><td>0.61 ± 0.00</td><td>0.63 ± 0.03</td><td>0.92 ± 0.00</td><td>0.85 ± 0.01</td></tr><tr><td>TabDDPM</td><td>0.66 ± 0.01</td><td>0.62 ± 0.00</td><td>0.67 ± 0.00</td><td>0.98 ± 0.00</td><td>0.95 ± 0.00</td></tr></tbody></table>
Results per datasets and models under diverse metrics for the *base models* (continued).

<table><caption>**Table E.15:** Results for *base models*. Models are trained using their default hyperparameters as provided by the authors in their papers. The best values per metric are formatted in **bold green** and the worse values are in **red**.</caption><thead><tr><th rowspan="2">Dataset</th><th rowspan="2">Model</th><th colspan="5">Metrics</th></tr><tr><th>C2ST ↓</th><th>DCR-Rate ↓</th><th>ML-Efficacy ↑</th><th>Shape ↑</th><th>Pair ↑</th></tr></thead><tbody><tr><td rowspan="5">House 16h</td><td>Train Copy</td><td>0.50 ± 0.01</td><td>1.00 ± 0.00</td><td>0.64 ± 0.01</td><td>0.99 ± 0.01</td><td>0.99 ± 0.00</td></tr><tr><td>CTGAN</td><td>1.00 ± 0.00</td><td>0.61 ± 0.02</td><td>0.20 ± 0.05</td><td>0.86 ± 0.01</td><td>0.95 ± 0.01</td></tr><tr><td>TVAE</td><td>0.98 ± 0.00</td><td>0.61 ± 0.01</td><td>0.36 ± 0.02</td><td>0.89 ± 0.00</td><td>0.96 ± 0.01</td></tr><tr><td>TabDDPM</td><td>0.63 ± 0.01</td><td>0.61 ± 0.01</td><td>0.57 ± 0.01</td><td>0.98 ± 0.00</td><td>0.97 ± 0.01</td></tr><tr><td>TabSyn</td><td>0.84 ± 0.03</td><td>0.62 ± 0.00</td><td>0.33 ± 0.06</td><td>0.96 ± 0.01</td><td>0.98 ± 0.01</td></tr><tr><td rowspan="5">Insurance</td><td>Train Copy</td><td>0.48 ± 0.01</td><td>1.00 ± 0.00</td><td>0.85 ± 0.03</td><td>0.96 ± 0.01</td><td>0.91 ± 0.01</td></tr><tr><td>CTGAN</td><td>0.92 ± 0.01</td><td>0.67 ± 0.06</td><td>-0.18 ± 0.05</td><td>0.84 ± 0.00</td><td>0.81 ± 0.01</td></tr><tr><td>TVAE</td><td>0.87 ± 0.02</td><td>0.62 ± 0.02</td><td>0.61 ± 0.03</td><td>0.85 ± 0.03</td><td>0.77 ± 0.03</td></tr><tr><td>TabDDPM</td><td>0.58 ± 0.01</td><td>0.60 ± 0.02</td><td>0.83 ± 0.02</td><td>0.95 ± 0.01</td><td>0.90 ± 0.01</td></tr><tr><td>TabSyn</td><td>0.60 ± 0.03</td><td>0.61 ± 0.02</td><td>0.83 ± 0.01</td><td>0.94 ± 0.01</td><td>0.89 ± 0.01</td></tr><tr><td rowspan="5">King</td><td>Train Copy</td><td>0.50 ± 0.01</td><td>1.00 ± 0.00</td><td>0.87 ± 0.00</td><td>0.98 ± 0.01</td><td>0.97 ± 0.01</td></tr><tr><td>CTGAN</td><td>1.00 ± 0.00</td><td>0.60 ± 0.01</td><td>0.54 ± 0.04</td><td>0.89 ± 0.01</td><td>0.93 ± 0.00</td></tr><tr><td>TVAE</td><td>0.99 ± 0.01</td><td>0.60 ± 0.00</td><td>0.70 ± 0.02</td><td>0.92 ± 0.01</td><td>0.91 ± 0.01</td></tr><tr><td>TabDDPM</td><td>1.00 ± 0.00</td><td>0.91 ± 0.14</td><td>-192.96 ± 153.37</td><td>0.33 ± 0.03</td><td>0.74 ± 0.02</td></tr><tr><td>TabSyn</td><td>0.97 ± 0.01</td><td>0.62 ± 0.01</td><td>0.05 ± 0.04</td><td>0.96 ± 0.01</td><td>0.94 ± 0.00</td></tr><tr><td rowspan="5">Minibone</td><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.89 ± 0.01</td><td>0.99 ± 0.00</td><td>0.99 ± 0.01</td></tr><tr><td>CTGAN</td><td>1.00 ± 0.00</td><td>0.60 ± 0.00</td><td>0.54 ± 0.05</td><td>0.80 ± 0.03</td><td>0.56 ± 0.01</td></tr><tr><td>TVAE</td><td>1.00 ± 0.00</td><td>0.60 ± 0.00</td><td>0.82 ± 0.01</td><td>0.91 ± 0.02</td><td>0.56 ± 0.00</td></tr><tr><td>TabDDPM</td><td>0.82 ± 0.01</td><td>0.63 ± 0.01</td><td>0.88 ± 0.00</td><td>0.95 ± 0.02</td><td>0.83 ± 0.03</td></tr><tr><td>TabSyn</td><td>0.71 ± 0.09</td><td>0.60 ± 0.00</td><td>0.89 ± 0.01</td><td>0.98 ± 0.01</td><td>0.89 ± 0.05</td></tr><tr><td rowspan="5">Moons</td><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>1.00 ± 0.00</td><td>0.99 ± 0.00</td><td>0.99 ± 0.00</td></tr><tr><td>CTGAN</td><td>0.93 ± 0.01</td><td>0.60 ± 0.05</td><td>1.00 ± 0.00</td><td>0.94 ± 0.01</td><td>0.70 ± 0.03</td></tr><tr><td>TVAE</td><td>0.82 ± 0.02</td><td>0.61 ± 0.03</td><td>1.00 ± 0.00</td><td>0.97 ± 0.01</td><td>0.76 ± 0.02</td></tr><tr><td>TabDDPM</td><td>0.61 ± 0.16</td><td>0.53 ± 0.15</td><td>0.97 ± 0.06</td><td>0.93 ± 0.10</td><td>0.90 ± 0.16</td></tr><tr><td>TabSyn</td><td>0.58 ± 0.03</td><td>0.61 ± 0.01</td><td>1.00 ± 0.00</td><td>0.98 ± 0.01</td><td>0.98 ± 0.01</td></tr></tbody></table>
Results per datasets and models under diverse metrics for the base models (continued).

<table><thead><tr><th rowspan="2">Dataset</th><th rowspan="2">Model</th><th colspan="5">Metrics</th></tr><tr><th>C2ST ↓</th><th>DCR-Rate ↓</th><th>ML-Efficacy ↑</th><th>Shape ↑</th><th>Pair ↑</th></tr></thead><tbody><tr><td rowspan="5">Bank marketing</td><td>TabSyn</td><td>0.71 ± 0.06</td><td>0.62 ± 0.00</td><td>0.66 ± 0.01</td><td>0.98 ± 0.01</td><td>0.95 ± 0.02</td></tr><tr><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.54 ± 0.01</td><td>0.99 ± 0.00</td><td>0.98 ± 0.01</td></tr><tr><td>CTGAN</td><td>0.89 ± 0.01</td><td>0.62 ± 0.01</td><td>0.33 ± 0.05</td><td>0.92 ± 0.00</td><td>0.86 ± 0.01</td></tr><tr><td>TVAE</td><td>0.95 ± 0.00</td><td>0.62 ± 0.00</td><td>0.52 ± 0.02</td><td>0.91 ± 0.01</td><td>0.84 ± 0.02</td></tr><tr><td>TabDDPM</td><td>0.68 ± 0.01</td><td>0.63 ± 0.01</td><td>0.48 ± 0.02</td><td>0.99 ± 0.01</td><td>0.96 ± 0.00</td></tr><tr><td rowspan="5">Bike sharing</td><td>TabSyn</td><td>0.65 ± 0.04</td><td>0.63 ± 0.01</td><td>0.47 ± 0.01</td><td>0.98 ± 0.01</td><td>0.96 ± 0.00</td></tr><tr><td>Train Copy</td><td>0.50 ± 0.01</td><td>1.00 ± 0.00</td><td>0.94 ± 0.00</td><td>0.99 ± 0.00</td><td>0.53 ± 0.00</td></tr><tr><td>CTGAN</td><td>1.00 ± 0.00</td><td>0.61 ± 0.00</td><td>0.37 ± 0.03</td><td>0.93 ± 0.01</td><td>0.51 ± 0.01</td></tr><tr><td>TVAE</td><td>1.00 ± 0.00</td><td>0.61 ± 0.01</td><td>0.42 ± 0.08</td><td>0.91 ± 0.01</td><td>0.51 ± 0.01</td></tr><tr><td>TabDDPM</td><td>0.85 ± 0.01</td><td>0.61 ± 0.00</td><td>0.67 ± 0.03</td><td>0.98 ± 0.00</td><td>0.53 ± 0.00</td></tr><tr><td rowspan="5">Black friday</td><td>TabSyn</td><td>0.94 ± 0.03</td><td>0.61 ± 0.00</td><td>0.31 ± 0.04</td><td>0.95 ± 0.01</td><td>0.52 ± 0.01</td></tr><tr><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.53 ± 0.01</td><td>1.00 ± 0.00</td><td>0.99 ± 0.00</td></tr><tr><td>CTGAN</td><td>0.92 ± 0.01</td><td>0.66 ± 0.01</td><td>0.40 ± 0.01</td><td>0.94 ± 0.01</td><td>0.84 ± 0.01</td></tr><tr><td>TVAE</td><td>0.98 ± 0.00</td><td>0.67 ± 0.01</td><td>0.29 ± 0.08</td><td>0.83 ± 0.01</td><td>0.73 ± 0.01</td></tr><tr><td>TabDDPM</td><td>0.92 ± 0.00</td><td>0.67 ± 0.01</td><td>0.31 ± 0.03</td><td>0.99 ± 0.00</td><td>0.98 ± 0.00</td></tr><tr><td rowspan="5">Cardio</td><td>TabSyn</td><td>0.91 ± 0.01</td><td>0.68 ± 0.00</td><td>0.13 ± 0.03</td><td>0.98 ± 0.00</td><td>0.96 ± 0.01</td></tr><tr><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.72 ± 0.01</td><td>1.00 ± 0.00</td><td>0.98 ± 0.01</td></tr><tr><td>CTGAN</td><td>1.00 ± 0.01</td><td>0.62 ± 0.01</td><td>0.67 ± 0.02</td><td>0.93 ± 0.01</td><td>0.93 ± 0.01</td></tr><tr><td>TVAE</td><td>1.00 ± 0.00</td><td>0.63 ± 0.00</td><td>0.67 ± 0.04</td><td>0.88 ± 0.01</td><td>0.90 ± 0.02</td></tr><tr><td>TabDDPM</td><td>0.59 ± 0.00</td><td>0.64 ± 0.00</td><td>0.72 ± 0.01</td><td>0.99 ± 0.00</td><td>0.96 ± 0.02</td></tr><tr><td rowspan="5">Churn</td><td>TabSyn</td><td>0.58 ± 0.01</td><td>0.64 ± 0.01</td><td>0.72 ± 0.01</td><td>0.99 ± 0.01</td><td>0.97 ± 0.01</td></tr><tr><td>Train Copy</td><td>0.50 ± 0.01</td><td>1.00 ± 0.00</td><td>0.59 ± 0.02</td><td>0.95 ± 0.00</td><td>0.87 ± 0.01</td></tr><tr><td>CTGAN</td><td>0.87 ± 0.02</td><td>0.60 ± 0.00</td><td>0.19 ± 0.10</td><td>0.85 ± 0.02</td><td>0.79 ± 0.00</td></tr><tr><td>TVAE</td><td>0.98 ± 0.01</td><td>0.60 ± 0.01</td><td>0.45 ± 0.10</td><td>0.75 ± 0.03</td><td>0.63 ± 0.03</td></tr><tr><td>TabDDPM</td><td>1.00 ± 0.00</td><td>0.65 ± 0.40</td><td>0.00 ± 0.00</td><td>0.59 ± 0.02</td><td>0.56 ± 0.02</td></tr><tr><td rowspan="5">Covertype</td><td>TabSyn</td><td>0.64 ± 0.03</td><td>0.61 ± 0.01</td><td>0.43 ± 0.13</td><td>0.92 ± 0.01</td><td>0.85 ± 0.00</td></tr><tr><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.90 ± 0.00</td><td>1.00 ± 0.00</td><td>1.00 ± 0.01</td></tr><tr><td>CTGAN</td><td>1.00 ± 0.00</td><td>0.60 ± 0.00</td><td>0.66 ± 0.01</td><td>0.97 ± 0.00</td><td>0.94 ± 0.01</td></tr><tr><td>TVAE</td><td>1.00 ± 0.00</td><td>0.60 ± 0.00</td><td>0.72 ± 0.01</td><td>0.98 ± 0.00</td><td>0.95 ± 0.01</td></tr><tr><td>TabDDPM</td><td>0.82 ± 0.01</td><td>0.60 ± 0.00</td><td>0.73 ± 0.01</td><td>1.00 ± 0.00</td><td>0.99 ± 0.00</td></tr><tr><td rowspan="5">Diamonds</td><td>TabSyn</td><td>0.72 ± 0.04</td><td>0.60 ± 0.00</td><td>0.79 ± 0.03</td><td>0.99 ± 0.00</td><td>0.99 ± 0.00</td></tr><tr><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.98 ± 0.00</td><td>0.99 ± 0.00</td><td>0.77 ± 0.01</td></tr><tr><td>CTGAN</td><td>0.98 ± 0.00</td><td>0.60 ± 0.00</td><td>0.87 ± 0.01</td><td>0.91 ± 0.01</td><td>0.75 ± 0.04</td></tr><tr><td>TVAE</td><td>0.97 ± 0.01</td><td>0.60 ± 0.01</td><td>0.91 ± 0.01</td><td>0.92 ± 0.02</td><td>0.76 ± 0.03</td></tr><tr><td>TabDDPM</td><td>0.76 ± 0.01</td><td>0.61 ± 0.00</td><td>0.97 ± 0.00</td><td>0.99 ± 0.01</td><td>0.71 ± 0.01</td></tr><tr><td rowspan="5">Heloc</td><td>TabSyn</td><td>0.95 ± 0.02</td><td>0.64 ± 0.00</td><td>0.19 ± 0.06</td><td>0.96 ± 0.00</td><td>0.72 ± 0.01</td></tr><tr><td>Train Copy</td><td>0.50 ± 0.01</td><td>1.00 ± 0.00</td><td>0.70 ± 0.01</td><td>0.99 ± 0.00</td><td>0.97 ± 0.01</td></tr><tr><td>CTGAN</td><td>1.00 ± 0.00</td><td>0.63 ± 0.00</td><td>0.40 ± 0.14</td><td>0.87 ± 0.05</td><td>0.87 ± 0.07</td></tr><tr><td>TVAE</td><td>0.98 ± 0.01</td><td>0.63 ± 0.02</td><td>0.69 ± 0.01</td><td>0.90 ± 0.00</td><td>0.75 ± 0.01</td></tr><tr><td>TabDDPM</td><td>0.71 ± 0.01</td><td>0.64 ± 0.02</td><td>0.70 ± 0.01</td><td>0.97 ± 0.00</td><td>0.94 ± 0.01</td></tr><tr><td rowspan="5">Higgs</td><td>TabSyn</td><td>0.75 ± 0.01</td><td>0.65 ± 0.01</td><td>0.69 ± 0.01</td><td>0.97 ± 0.00</td><td>0.96 ± 0.01</td></tr><tr><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.74 ± 0.00</td><td>0.99 ± 0.00</td><td>0.99 ± 0.00</td></tr><tr><td>CTGAN</td><td>1.00 ± 0.00</td><td>0.60 ± 0.00</td><td>0.61 ± 0.08</td><td>0.87 ± 0.02</td><td>0.95 ± 0.00</td></tr><tr><td>TVAE</td><td>1.00 ± 0.00</td><td>0.61 ± 0.02</td><td>0.68 ± 0.02</td><td>0.78 ± 0.00</td><td>0.94 ± 0.01</td></tr><tr><td>TabDDPM</td><td>0.79 ± 0.02</td><td>0.60 ± 0.01</td><td>0.72 ± 0.01</td><td>0.98 ± 0.01</td><td>0.93 ± 0.02</td></tr><tr><td></td><td>TabSyn</td><td>0.59 ± 0.01</td><td>0.61 ± 0.00</td><td>0.73 ± 0.00</td><td>0.94 ± 0.00</td><td>0.99 ± 0.00</td></tr></tbody></table>
Appendix F. Quick Search on Reduced Hyperparameter Space

With the reduced hyperparameters search spaces presented in Appendix A, we ran a *light* hyperparameter tuning described in Section 5. The experiment was done on all dataset (Table 2). We performed 50 trials per fold with 3 fold, meaning we ran a total of 150 trials for this light experiment. The results per datasets are shown in Table F.16.

<table><thead><tr><th rowspan="2">Dataset</th><th rowspan="2">Model</th><th colspan="6">Metrics</th></tr><tr><th>C2ST ↓</th><th>DCR-Rate ↓</th><th>ML-Efficacy ↑</th><th>Shape ↑</th><th>Pair ↑</th><th>Sampling time ↓</th></tr></thead><tbody><tr><td rowspan="5">Abalone</td><td>Train Copy</td><td>0.51 ± 0.00</td><td>1.00 ± 0.00</td><td>0.23 ± 0.01</td><td>0.96 ± 0.01</td><td>0.88 ± 0.01</td><td>-</td></tr><tr><td>CTGAN</td><td>0.71 ± 0.03</td><td>0.63 ± 0.00</td><td>0.17 ± 0.01</td><td>0.93 ± 0.02</td><td>0.86 ± 0.04</td><td>00 ± 0.01</td></tr><tr><td>TVAE</td><td>0.64 ± 0.02</td><td>0.67 ± 0.00</td><td>0.23 ± 0.01</td><td>0.93 ± 0.02</td><td>0.89 ± 0.03</td><td>00 ± 0.00</td></tr><tr><td>TabDDPM</td><td>0.78 ± 0.01</td><td>0.69 ± 0.03</td><td>0.23 ± 0.01</td><td>0.95 ± 0.00</td><td>0.88 ± 0.02</td><td>03 ± 0.88</td></tr><tr><td>TabSyn</td><td>0.80 ± 0.00</td><td>0.62 ± 0.01</td><td>0.19 ± 0.03</td><td>0.93 ± 0.01</td><td>0.85 ± 0.01</td><td>00 ± 0.01</td></tr><tr><td rowspan="5">Adult</td><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.71 ± 0.01</td><td>0.99 ± 0.00</td><td>0.98 ± 0.00</td><td>-</td></tr><tr><td>CTGAN</td><td>0.77 ± 0.01</td><td>0.72 ± 0.00</td><td>0.65 ± 0.00</td><td>0.96 ± 0.01</td><td>0.89 ± 0.02</td><td>00 ± 0.02</td></tr><tr><td>TVAE</td><td>0.77 ± 0.01</td><td>0.72 ± 0.01</td><td>0.65 ± 0.02</td><td>0.96 ± 0.01</td><td>0.93 ± 0.00</td><td>00 ± 0.00</td></tr><tr><td>TabDDPM</td><td>0.67 ± 0.01</td><td>0.62 ± 0.00</td><td>0.67 ± 0.01</td><td>0.97 ± 0.01</td><td>0.94 ± 0.01</td><td>11 ± 0.63</td></tr><tr><td>TabSyn</td><td>0.73 ± 0.01</td><td>0.62 ± 0.00</td><td>0.66 ± 0.01</td><td>0.97 ± 0.01</td><td>0.94 ± 0.01</td><td>02 ± 0.01</td></tr><tr><td rowspan="5">Bank marketing</td><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.54 ± 0.01</td><td>0.99 ± 0.00</td><td>0.98 ± 0.01</td><td>-</td></tr><tr><td>CTGAN</td><td>0.72 ± 0.01</td><td>0.63 ± 0.00</td><td>0.45 ± 0.04</td><td>0.98 ± 0.00</td><td>0.94 ± 0.01</td><td>00 ± 0.01</td></tr><tr><td>TVAE</td><td>0.78 ± 0.02</td><td>0.63 ± 0.00</td><td>0.47 ± 0.03</td><td>0.97 ± 0.01</td><td>0.94 ± 0.00</td><td>00 ± 0.00</td></tr><tr><td>TabDDPM</td><td>0.68 ± 0.00</td><td>0.63 ± 0.01</td><td>0.52 ± 0.03</td><td>0.97 ± 0.00</td><td>0.95 ± 0.01</td><td>16 ± 2.18</td></tr><tr><td>TabSyn</td><td>0.75 ± 0.00</td><td>0.62 ± 0.00</td><td>0.42 ± 0.04</td><td>0.97 ± 0.01</td><td>0.95 ± 0.00</td><td>02 ± 0.01</td></tr><tr><td rowspan="5">Bike sharing</td><td>Train Copy</td><td>0.50 ± 0.01</td><td>1.00 ± 0.00</td><td>0.94 ± 0.00</td><td>0.99 ± 0.00</td><td>0.53 ± 0.00</td><td>-</td></tr><tr><td>CTGAN</td><td>0.89 ± 0.01</td><td>0.61 ± 0.01</td><td>0.71 ± 0.01</td><td>0.98 ± 0.01</td><td>0.53 ± 0.00</td><td>00 ± 0.00</td></tr><tr><td>TVAE</td><td>0.81 ± 0.01</td><td>0.61 ± 0.01</td><td>0.69 ± 0.03</td><td>0.96 ± 0.00</td><td>0.53 ± 0.00</td><td>00 ± 0.00</td></tr><tr><td>TabDDPM</td><td>0.80 ± 0.02</td><td>0.63 ± 0.01</td><td>0.83 ± 0.01</td><td>0.96 ± 0.02</td><td>0.53 ± 0.01</td><td>06 ± 1.34</td></tr><tr><td>TabSyn</td><td>0.91 ± 0.01</td><td>0.61 ± 0.01</td><td>0.32 ± 0.06</td><td>0.95 ± 0.01</td><td>0.52 ± 0.00</td><td>00 ± 0.01</td></tr><tr><td rowspan="5">Black friday</td><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.53 ± 0.01</td><td>1.00 ± 0.00</td><td>0.99 ± 0.00</td><td>-</td></tr><tr><td>CTGAN</td><td>0.87 ± 0.01</td><td>0.68 ± 0.00</td><td>0.36 ± 0.01</td><td>0.97 ± 0.01</td><td>0.91 ± 0.02</td><td>01 ± 0.17</td></tr><tr><td>TVAE</td><td>0.95 ± 0.01</td><td>0.68 ± 0.00</td><td>0.27 ± 0.02</td><td>0.97 ± 0.00</td><td>0.95 ± 0.00</td><td>00 ± 0.02</td></tr><tr><td>TabDDPM</td><td>0.89 ± 0.01</td><td>0.67 ± 0.00</td><td>0.44 ± 0.02</td><td>0.97 ± 0.01</td><td>0.96 ± 0.01</td><td>50 ± 17.19</td></tr><tr><td>TabSyn</td><td>0.89 ± 0.01</td><td>0.68 ± 0.00</td><td>0.16 ± 0.01</td><td>0.97 ± 0.01</td><td>0.95 ± 0.01</td><td>07 ± 0.01</td></tr><tr><td rowspan="5">Cardio</td><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.72 ± 0.01</td><td>1.00 ± 0.00</td><td>0.98 ± 0.01</td><td>-</td></tr><tr><td>CTGAN</td><td>0.64 ± 0.01</td><td>0.64 ± 0.01</td><td>0.72 ± 0.01</td><td>0.99 ± 0.00</td><td>0.96 ± 0.00</td><td>00 ± 0.06</td></tr><tr><td>TVAE</td><td>0.71 ± 0.01</td><td>0.64 ± 0.01</td><td>0.73 ± 0.01</td><td>0.96 ± 0.01</td><td>0.96 ± 0.01</td><td>00 ± 0.01</td></tr><tr><td>TabDDPM</td><td>0.57 ± 0.01</td><td>0.64 ± 0.00</td><td>0.72 ± 0.01</td><td>0.99 ± 0.00</td><td>0.98 ± 0.01</td><td>12 ± 4.58</td></tr><tr><td>TabSyn</td><td>0.59 ± 0.01</td><td>0.64 ± 0.00</td><td>0.72 ± 0.01</td><td>0.98 ± 0.01</td><td>0.97 ± 0.01</td><td>03 ± 0.01</td></tr><tr><td rowspan="5">Churn</td><td>Train Copy</td><td>0.50 ± 0.01</td><td>1.00 ± 0.00</td><td>0.59 ± 0.02</td><td>0.95 ± 0.00</td><td>0.87 ± 0.01</td><td>-</td></tr><tr><td>CTGAN</td><td>0.63 ± 0.01</td><td>0.63 ± 0.01</td><td>0.39 ± 0.01</td><td>0.93 ± 0.00</td><td>0.84 ± 0.01</td><td>00 ± 0.01</td></tr><tr><td>TVAE</td><td>0.64 ± 0.00</td><td>0.63 ± 0.01</td><td>0.53 ± 0.01</td><td>0.92 ± 0.00</td><td>0.84 ± 0.00</td><td>00 ± 0.00</td></tr><tr><td>TabDDPM</td><td>0.98 ± 0.03</td><td>0.67 ± 0.18</td><td>0.02 ± 0.03</td><td>0.59 ± 0.05</td><td>0.55 ± 0.02</td><td>18 ± 1.06</td></tr><tr><td>TabSyn</td><td>0.68 ± 0.06</td><td>0.61 ± 0.00</td><td>0.46 ± 0.03</td><td>0.91 ± 0.01</td><td>0.84 ± 0.01</td><td>00 ± 0.01</td></tr></tbody></table>
Results per datasets and models under diverse metrics for the *base models* (continued).

<table><caption>**Table E.15:** Results for *base models*. Models are trained using their default hyperparameters as provided by the authors in their papers. The best values per metric are formatted in **bold green** and the worse values are in **red**.</caption><thead><tr><th rowspan="2">Dataset</th><th rowspan="2">Model</th><th colspan="5">Metrics</th></tr><tr><th>C2ST ↓</th><th>DCR-Rate ↓</th><th>ML-Efficacy ↑</th><th>Shape ↑</th><th>Pair ↑</th></tr></thead><tbody><tr><td rowspan="5">House 16h</td><td>Train Copy</td><td>0.50 ± 0.01</td><td>1.00 ± 0.00</td><td>0.64 ± 0.01</td><td>0.99 ± 0.01</td><td>0.99 ± 0.00</td></tr><tr><td>CTGAN</td><td>1.00 ± 0.00</td><td>0.61 ± 0.02</td><td>0.20 ± 0.05</td><td>0.86 ± 0.01</td><td>0.95 ± 0.01</td></tr><tr><td>TVAE</td><td>0.98 ± 0.00</td><td>0.61 ± 0.01</td><td>0.36 ± 0.02</td><td>0.89 ± 0.00</td><td>0.96 ± 0.01</td></tr><tr><td>TabDDPM</td><td>0.63 ± 0.01</td><td>0.61 ± 0.01</td><td>0.57 ± 0.01</td><td>0.98 ± 0.00</td><td>0.97 ± 0.01</td></tr><tr><td>TabSyn</td><td>0.84 ± 0.03</td><td>0.62 ± 0.00</td><td>0.33 ± 0.06</td><td>0.96 ± 0.01</td><td>0.98 ± 0.01</td></tr><tr><td rowspan="5">Insurance</td><td>Train Copy</td><td>0.48 ± 0.01</td><td>1.00 ± 0.00</td><td>0.85 ± 0.03</td><td>0.96 ± 0.01</td><td>0.91 ± 0.01</td></tr><tr><td>CTGAN</td><td>0.92 ± 0.01</td><td>0.67 ± 0.06</td><td>-0.18 ± 0.05</td><td>0.84 ± 0.00</td><td>0.81 ± 0.01</td></tr><tr><td>TVAE</td><td>0.87 ± 0.02</td><td>0.62 ± 0.02</td><td>0.61 ± 0.03</td><td>0.85 ± 0.03</td><td>0.77 ± 0.03</td></tr><tr><td>TabDDPM</td><td>0.58 ± 0.01</td><td>0.60 ± 0.02</td><td>0.83 ± 0.02</td><td>0.95 ± 0.01</td><td>0.90 ± 0.01</td></tr><tr><td>TabSyn</td><td>0.60 ± 0.03</td><td>0.61 ± 0.02</td><td>0.83 ± 0.01</td><td>0.94 ± 0.01</td><td>0.89 ± 0.01</td></tr><tr><td rowspan="5">King</td><td>Train Copy</td><td>0.50 ± 0.01</td><td>1.00 ± 0.00</td><td>0.87 ± 0.00</td><td>0.98 ± 0.01</td><td>0.97 ± 0.01</td></tr><tr><td>CTGAN</td><td>1.00 ± 0.00</td><td>0.60 ± 0.01</td><td>0.54 ± 0.04</td><td>0.89 ± 0.01</td><td>0.93 ± 0.00</td></tr><tr><td>TVAE</td><td>0.99 ± 0.01</td><td>0.60 ± 0.00</td><td>0.70 ± 0.02</td><td>0.92 ± 0.01</td><td>0.91 ± 0.01</td></tr><tr><td>TabDDPM</td><td>1.00 ± 0.00</td><td>0.91 ± 0.14</td><td>-192.96 ± 153.37</td><td>0.33 ± 0.03</td><td>0.74 ± 0.02</td></tr><tr><td>TabSyn</td><td>0.97 ± 0.01</td><td>0.62 ± 0.01</td><td>0.05 ± 0.04</td><td>0.96 ± 0.01</td><td>0.94 ± 0.00</td></tr><tr><td rowspan="5">Minibone</td><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.89 ± 0.01</td><td>0.99 ± 0.00</td><td>0.99 ± 0.01</td></tr><tr><td>CTGAN</td><td>1.00 ± 0.00</td><td>0.60 ± 0.00</td><td>0.54 ± 0.05</td><td>0.80 ± 0.03</td><td>0.56 ± 0.01</td></tr><tr><td>TVAE</td><td>1.00 ± 0.00</td><td>0.60 ± 0.00</td><td>0.82 ± 0.01</td><td>0.91 ± 0.02</td><td>0.56 ± 0.00</td></tr><tr><td>TabDDPM</td><td>0.82 ± 0.01</td><td>0.63 ± 0.01</td><td>0.88 ± 0.00</td><td>0.95 ± 0.02</td><td>0.83 ± 0.03</td></tr><tr><td>TabSyn</td><td>0.71 ± 0.09</td><td>0.60 ± 0.00</td><td>0.89 ± 0.01</td><td>0.98 ± 0.01</td><td>0.89 ± 0.05</td></tr><tr><td rowspan="5">Moons</td><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>1.00 ± 0.00</td><td>0.99 ± 0.00</td><td>0.99 ± 0.00</td></tr><tr><td>CTGAN</td><td>0.93 ± 0.01</td><td>0.60 ± 0.05</td><td>1.00 ± 0.00</td><td>0.94 ± 0.01</td><td>0.70 ± 0.03</td></tr><tr><td>TVAE</td><td>0.82 ± 0.02</td><td>0.61 ± 0.03</td><td>1.00 ± 0.00</td><td>0.97 ± 0.01</td><td>0.76 ± 0.02</td></tr><tr><td>TabDDPM</td><td>0.61 ± 0.16</td><td>0.53 ± 0.15</td><td>0.97 ± 0.06</td><td>0.93 ± 0.10</td><td>0.90 ± 0.16</td></tr><tr><td>TabSyn</td><td>0.58 ± 0.03</td><td>0.61 ± 0.01</td><td>1.00 ± 0.00</td><td>0.98 ± 0.01</td><td>0.98 ± 0.01</td></tr></tbody></table>
Results per datasets and models under diverse metrics for the light search (continued).

<table><thead><tr><th rowspan="2">Dataset</th><th rowspan="2">Model</th><th colspan="6">Metrics</th></tr><tr><th>C2ST ↓</th><th>DCR-Rate ↓</th><th>ML-Efficacy ↑</th><th>Shape ↑</th><th>Pair ↑</th><th>Sampling time ↓</th></tr></thead><tbody><tr><td rowspan="4">Covertype</td><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.90 ± 0.00</td><td>1.00 ± 0.00</td><td>1.00 ± 0.01</td><td>-</td></tr><tr><td>CTGAN</td><td>0.98 ± 0.00</td><td>0.60 ± 0.00</td><td>0.69 ± 0.00</td><td>0.98 ± 0.00</td><td>0.95 ± 0.01</td><td>0.6 ± 1.58</td></tr><tr><td>TVAE</td><td>0.90 ± 0.01</td><td>0.60 ± 0.00</td><td>0.77 ± 0.01</td><td>0.98 ± 0.00</td><td>0.96 ± 0.00</td><td>0.2 ± 0.07</td></tr><tr><td>TabDDPM</td><td>0.97 ± 0.01</td><td>0.64 ± 0.02</td><td>0.69 ± 0.00</td><td>0.94 ± 0.02</td><td>0.89 ± 0.03</td><td>355 ± 10.90</td></tr><tr><td rowspan="4">Diamonds</td><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.98 ± 0.00</td><td>0.99 ± 0.00</td><td>0.77 ± 0.01</td><td>-</td></tr><tr><td>CTGAN</td><td>0.89 ± 0.01</td><td>0.64 ± 0.01</td><td>0.94 ± 0.00</td><td>0.95 ± 0.00</td><td>0.74 ± 0.02</td><td>0.0 ± 0.08</td></tr><tr><td>TVAE</td><td>0.76 ± 0.02</td><td>0.64 ± 0.00</td><td>0.96 ± 0.01</td><td>0.95 ± 0.01</td><td>0.73 ± 0.01</td><td>00 ± 0.01</td></tr><tr><td>TabDDPM</td><td>0.75 ± 0.01</td><td>0.61 ± 0.01</td><td>0.97 ± 0.00</td><td>0.97 ± 0.01</td><td>0.70 ± 0.02</td><td>10 ± 1.26</td></tr><tr><td rowspan="4">Heloc</td><td>Train Copy</td><td>0.50 ± 0.01</td><td>1.00 ± 0.00</td><td>0.70 ± 0.01</td><td>0.99 ± 0.00</td><td>0.97 ± 0.01</td><td>-</td></tr><tr><td>CTGAN</td><td>0.93 ± 0.02</td><td>0.64 ± 0.01</td><td>0.70 ± 0.01</td><td>0.97 ± 0.00</td><td>0.93 ± 0.01</td><td>00 ± 0.02</td></tr><tr><td>TVAE</td><td>0.92 ± 0.01</td><td>0.63 ± 0.01</td><td>0.69 ± 0.02</td><td>0.94 ± 0.00</td><td>0.88 ± 0.01</td><td>00 ± 0.00</td></tr><tr><td>TabDDPM</td><td>0.71 ± 0.02</td><td>0.67 ± 0.01</td><td>0.69 ± 0.02</td><td>0.95 ± 0.01</td><td>0.92 ± 0.03</td><td>03 ± 1.99</td></tr><tr><td rowspan="4">Higgs</td><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.74 ± 0.00</td><td>0.99 ± 0.00</td><td>0.99 ± 0.00</td><td>-</td></tr><tr><td>CTGAN</td><td>0.87 ± 0.00</td><td>0.60 ± 0.01</td><td>0.70 ± 0.01</td><td>0.98 ± 0.00</td><td>0.98 ± 0.00</td><td>00 ± 0.09</td></tr><tr><td>TVAE</td><td>0.92 ± 0.01</td><td>0.60 ± 0.01</td><td>0.71 ± 0.02</td><td>0.94 ± 0.01</td><td>0.97 ± 0.00</td><td>00 ± 0.03</td></tr><tr><td>TabDDPM</td><td>0.61 ± 0.02</td><td>0.62 ± 0.01</td><td>0.73 ± 0.00</td><td>0.98 ± 0.01</td><td>0.95 ± 0.01</td><td>08 ± 1.00</td></tr><tr><td rowspan="4">House 16h</td><td>Train Copy</td><td>0.50 ± 0.01</td><td>1.00 ± 0.00</td><td>0.64 ± 0.01</td><td>0.99 ± 0.01</td><td>0.99 ± 0.00</td><td>-</td></tr><tr><td>CTGAN</td><td>0.84 ± 0.02</td><td>0.62 ± 0.00</td><td>0.45 ± 0.02</td><td>0.97 ± 0.01</td><td>0.97 ± 0.01</td><td>00 ± 0.01</td></tr><tr><td>TVAE</td><td>0.84 ± 0.00</td><td>0.62 ± 0.01</td><td>0.46 ± 0.03</td><td>0.94 ± 0.00</td><td>0.98 ± 0.00</td><td>00 ± 0.00</td></tr><tr><td>TabDDPM</td><td>0.64 ± 0.01</td><td>0.61 ± 0.01</td><td>0.61 ± 0.01</td><td>0.96 ± 0.01</td><td>0.94 ± 0.03</td><td>02 ± 0.75</td></tr><tr><td rowspan="4">Insurance</td><td>Train Copy</td><td>0.50 ± 0.01</td><td>1.00 ± 0.00</td><td>0.64 ± 0.01</td><td>0.99 ± 0.01</td><td>0.99 ± 0.00</td><td>-</td></tr><tr><td>CTGAN</td><td>0.67 ± 0.02</td><td>0.92 ± 0.01</td><td>0.66 ± 0.04</td><td>0.94 ± 0.01</td><td>0.85 ± 0.02</td><td>00 ± 0.01</td></tr><tr><td>TVAE</td><td>0.65 ± 0.02</td><td>0.91 ± 0.02</td><td>0.80 ± 0.03</td><td>0.93 ± 0.01</td><td>0.88 ± 0.01</td><td>00 ± 0.00</td></tr><tr><td>TabDDPM</td><td>0.61 ± 0.02</td><td>0.62 ± 0.02</td><td>0.83 ± 0.03</td><td>0.94 ± 0.01</td><td>0.89 ± 0.02</td><td>06 ± 2.76</td></tr><tr><td rowspan="4">King</td><td>Train Copy</td><td>0.50 ± 0.01</td><td>1.00 ± 0.00</td><td>0.87 ± 0.00</td><td>0.98 ± 0.01</td><td>0.97 ± 0.01</td><td>-</td></tr><tr><td>CTGAN</td><td>0.96 ± 0.01</td><td>0.62 ± 0.00</td><td>0.66 ± 0.03</td><td>0.97 ± 0.00</td><td>0.94 ± 0.01</td><td>00 ± 0.13</td></tr><tr><td>TVAE</td><td>0.95 ± 0.01</td><td>0.61 ± 0.01</td><td>0.80 ± 0.01</td><td>0.95 ± 0.01</td><td>0.94 ± 0.00</td><td>00 ± 0.01</td></tr><tr><td>TabDDPM</td><td>1.00 ± 0.00</td><td>0.70 ± 0.46</td><td>0.03 ± 0.68</td><td>0.28 ± 0.07</td><td>0.76 ± 0.00</td><td>05 ± 0.43</td></tr><tr><td rowspan="4">Miniboo ne</td><td>Train Copy</td><td>0.50 ± 0.01</td><td>1.00 ± 0.00</td><td>0.87 ± 0.00</td><td>0.98 ± 0.01</td><td>0.97 ± 0.01</td><td>-</td></tr><tr><td>CTGAN</td><td>0.90 ± 0.01</td><td>0.60 ± 0.01</td><td>0.87 ± 0.01</td><td>0.93 ± 0.01</td><td>0.58 ± 0.01</td><td>01 ± 0.03</td></tr><tr><td>TVAE</td><td>0.94 ± 0.01</td><td>0.60 ± 0.00</td><td>0.87 ± 0.00</td><td>0.94 ± 0.00</td><td>0.59 ± 0.01</td><td>00 ± 0.03</td></tr><tr><td>TabDDPM</td><td>0.73 ± 0.01</td><td>0.62 ± 0.00</td><td>0.89 ± 0.01</td><td>0.96 ± 0.01</td><td>0.83 ± 0.05</td><td>12 ± 1.35</td></tr><tr><td></td><td>TabSyn</td><td>0.87 ± 0.01</td><td>0.60 ± 0.01</td><td>0.87 ± 0.00</td><td>0.96 ± 0.00</td><td>0.76 ± 0.14</td><td>06 ± 0.08</td></tr></tbody></table>
Appendix F. Quick Search on Reduced Hyperparameter Space

<figure><img src="image_13.png" /><figcaption>**Figure F.12:** Models' ranking under the *light* (limited-budget) experiment setup with critical difference diagrams on C2ST, *column-wise similarity*, *pair-wise correlation*, DCR-Rate, and ML-Efficacy metrics over all datasets.</figcaption></figure>

With the reduced hyperparameters search spaces presented in Appendix A, we ran a limited-budget hyperparameter tuning described in Section 5. The experiment was done on all dataset (Table 2). We performed 50 trials per fold with 3 folds, meaning we ran a total of 150 trials for this limited-budget experiment. The results per datasets are shown in Table F.16.
Results per datasets and models under diverse metrics for the light search (continued).

<table><caption>**Table F.16:** Light experiment results under various metrics. Results are averaged over 3 folds with 5 synthetic samples per fold as done in the extensive hyperparameter tuning. The best values per metric are formatted in **bold green** and the worse values are in **red**.</caption><thead><tr><th rowspan="2">Dataset</th><th rowspan="2">Model</th><th colspan="6">Metrics</th></tr><tr><th>C2ST ↓</th><th>DCR-Rate ↓</th><th>ML-Efficacy ↑</th><th>Shape ↑</th><th>Pair ↑</th><th>Sampling time ↓</th></tr></thead><tbody><tr><td rowspan="4">Moons</td><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>1.00 ± 0.00</td><td>0.99 ± 0.00</td><td>0.99 ± 0.00</td><td>-</td></tr><tr><td>CTGAN</td><td>0.70 ± 0.02</td><td>0.62 ± 0.02</td><td>1.00 ± 0.00</td><td>0.96 ± 0.01</td><td>0.96 ± 0.01</td><td>0.00 ± 0.02</td></tr><tr><td>TVAE</td><td>0.69 ± 0.01</td><td>0.62 ± 0.01</td><td>1.00 ± 0.00</td><td>0.96 ± 0.01</td><td>0.93 ± 0.02</td><td>0.00 ± 0.00</td></tr><tr><td>TabDDPM</td><td>0.53 ± 0.01</td><td>0.61 ± 0.01</td><td>1.00 ± 0.00</td><td>0.99 ± 0.00</td><td>0.98 ± 0.01</td><td>0.08 ± 2.13</td></tr><tr><td></td><td>TabSyn</td><td>0.59 ± 0.01</td><td>0.61 ± 0.01</td><td>1.00 ± 0.00</td><td>0.98 ± 0.01</td><td>0.97 ± 0.01</td><td>0.01 ± 0.00</td></tr></tbody></table>
<table><thead><tr><th rowspan="2">Dataset</th><th rowspan="2">Model</th><th colspan="6">Metrics</th></tr><tr><th>C2ST ↓</th><th>DCR-Rate ↓</th><th>ML-Efficacy ↑</th><th>Shape ↑</th><th>Pair ↑</th><th>Sampling time ↓</th></tr></thead><tbody><tr><td rowspan="5">Abalone</td><td>Train Copy</td><td>0.51 ± 0.00</td><td>1.00 ± 0.00</td><td>0.23 ± 0.01</td><td>0.96 ± 0.01</td><td>0.88 ± 0.01</td><td>-</td></tr><tr><td>CTGAN</td><td>0.71 ± 0.03</td><td>0.63 ± 0.00</td><td>0.17 ± 0.01</td><td>0.93 ± 0.02</td><td>0.86 ± 0.04</td><td>00 ± 0.01</td></tr><tr><td>TVAE</td><td>0.64 ± 0.02</td><td>0.67 ± 0.00</td><td>0.23 ± 0.01</td><td>0.93 ± 0.02</td><td>0.89 ± 0.03</td><td>00 ± 0.00</td></tr><tr><td>TabDDPM</td><td>0.78 ± 0.01</td><td>0.69 ± 0.03</td><td>0.23 ± 0.01</td><td>0.95 ± 0.00</td><td>0.88 ± 0.02</td><td>03 ± 0.88</td></tr><tr><td>TabSyn</td><td>0.80 ± 0.00</td><td>0.62 ± 0.01</td><td>0.19 ± 0.03</td><td>0.93 ± 0.01</td><td>0.85 ± 0.01</td><td>00 ± 0.01</td></tr><tr><td rowspan="5">Adult</td><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.71 ± 0.01</td><td>0.99 ± 0.00</td><td>0.98 ± 0.00</td><td>-</td></tr><tr><td>CTGAN</td><td>0.77 ± 0.01</td><td>0.72 ± 0.00</td><td>0.65 ± 0.00</td><td>0.96 ± 0.01</td><td>0.89 ± 0.02</td><td>00 ± 0.02</td></tr><tr><td>TVAE</td><td>0.77 ± 0.01</td><td>0.72 ± 0.01</td><td>0.65 ± 0.02</td><td>0.96 ± 0.01</td><td>0.93 ± 0.00</td><td>00 ± 0.00</td></tr><tr><td>TabDDPM</td><td>0.67 ± 0.01</td><td>0.62 ± 0.00</td><td>0.67 ± 0.01</td><td>0.97 ± 0.01</td><td>0.94 ± 0.01</td><td>11 ± 0.63</td></tr><tr><td>TabSyn</td><td>0.73 ± 0.01</td><td>0.62 ± 0.00</td><td>0.66 ± 0.01</td><td>0.97 ± 0.01</td><td>0.94 ± 0.01</td><td>02 ± 0.01</td></tr><tr><td rowspan="5">Bank marketing</td><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.54 ± 0.01</td><td>0.99 ± 0.00</td><td>0.98 ± 0.01</td><td>-</td></tr><tr><td>CTGAN</td><td>0.72 ± 0.01</td><td>0.63 ± 0.00</td><td>0.45 ± 0.04</td><td>0.98 ± 0.00</td><td>0.94 ± 0.01</td><td>00 ± 0.01</td></tr><tr><td>TVAE</td><td>0.78 ± 0.02</td><td>0.63 ± 0.00</td><td>0.47 ± 0.03</td><td>0.97 ± 0.01</td><td>0.94 ± 0.00</td><td>00 ± 0.00</td></tr><tr><td>TabDDPM</td><td>0.68 ± 0.00</td><td>0.63 ± 0.01</td><td>0.52 ± 0.03</td><td>0.97 ± 0.00</td><td>0.95 ± 0.01</td><td>16 ± 2.18</td></tr><tr><td>TabSyn</td><td>0.75 ± 0.00</td><td>0.62 ± 0.00</td><td>0.42 ± 0.04</td><td>0.97 ± 0.01</td><td>0.95 ± 0.00</td><td>02 ± 0.01</td></tr><tr><td rowspan="5">Bike sharing</td><td>Train Copy</td><td>0.50 ± 0.01</td><td>1.00 ± 0.00</td><td>0.94 ± 0.00</td><td>0.99 ± 0.00</td><td>0.53 ± 0.00</td><td>-</td></tr><tr><td>CTGAN</td><td>0.89 ± 0.01</td><td>0.61 ± 0.01</td><td>0.71 ± 0.01</td><td>0.98 ± 0.01</td><td>0.53 ± 0.00</td><td>00 ± 0.00</td></tr><tr><td>TVAE</td><td>0.81 ± 0.01</td><td>0.61 ± 0.01</td><td>0.69 ± 0.03</td><td>0.96 ± 0.00</td><td>0.53 ± 0.00</td><td>00 ± 0.00</td></tr><tr><td>TabDDPM</td><td>0.80 ± 0.02</td><td>0.63 ± 0.01</td><td>0.83 ± 0.01</td><td>0.96 ± 0.02</td><td>0.53 ± 0.01</td><td>06 ± 1.34</td></tr><tr><td>TabSyn</td><td>0.91 ± 0.01</td><td>0.61 ± 0.01</td><td>0.32 ± 0.06</td><td>0.95 ± 0.01</td><td>0.52 ± 0.00</td><td>00 ± 0.01</td></tr><tr><td rowspan="5">Black friday</td><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.53 ± 0.01</td><td>1.00 ± 0.00</td><td>0.99 ± 0.00</td><td>-</td></tr><tr><td>CTGAN</td><td>0.87 ± 0.01</td><td>0.68 ± 0.00</td><td>0.36 ± 0.01</td><td>0.97 ± 0.01</td><td>0.91 ± 0.02</td><td>01 ± 0.17</td></tr><tr><td>TVAE</td><td>0.95 ± 0.01</td><td>0.68 ± 0.00</td><td>0.27 ± 0.02</td><td>0.97 ± 0.00</td><td>0.95 ± 0.00</td><td>00 ± 0.02</td></tr><tr><td>TabDDPM</td><td>0.89 ± 0.01</td><td>0.67 ± 0.00</td><td>0.44 ± 0.02</td><td>0.97 ± 0.01</td><td>0.96 ± 0.01</td><td>50 ± 17.19</td></tr><tr><td>TabSyn</td><td>0.89 ± 0.01</td><td>0.68 ± 0.00</td><td>0.16 ± 0.01</td><td>0.97 ± 0.01</td><td>0.95 ± 0.01</td><td>07 ± 0.01</td></tr><tr><td rowspan="5">Cardio</td><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.72 ± 0.01</td><td>1.00 ± 0.00</td><td>0.98 ± 0.01</td><td>-</td></tr><tr><td>CTGAN</td><td>0.64 ± 0.01</td><td>0.64 ± 0.01</td><td>0.72 ± 0.01</td><td>0.99 ± 0.00</td><td>0.96 ± 0.00</td><td>00 ± 0.06</td></tr><tr><td>TVAE</td><td>0.71 ± 0.01</td><td>0.64 ± 0.01</td><td>0.73 ± 0.01</td><td>0.96 ± 0.01</td><td>0.96 ± 0.01</td><td>00 ± 0.01</td></tr><tr><td>TabDDPM</td><td>0.57 ± 0.01</td><td>0.64 ± 0.00</td><td>0.72 ± 0.01</td><td>0.99 ± 0.00</td><td>0.98 ± 0.01</td><td>12 ± 4.58</td></tr><tr><td>TabSyn</td><td>0.59 ± 0.01</td><td>0.64 ± 0.00</td><td>0.72 ± 0.01</td><td>0.98 ± 0.01</td><td>0.97 ± 0.01</td><td>03 ± 0.01</td></tr><tr><td rowspan="5">Churn</td><td>Train Copy</td><td>0.50 ± 0.01</td><td>1.00 ± 0.00</td><td>0.59 ± 0.02</td><td>0.95 ± 0.00</td><td>0.87 ± 0.01</td><td>-</td></tr><tr><td>CTGAN</td><td>0.63 ± 0.01</td><td>0.63 ± 0.01</td><td>0.39 ± 0.01</td><td>0.93 ± 0.00</td><td>0.84 ± 0.01</td><td>00 ± 0.01</td></tr><tr><td>TVAE</td><td>0.64 ± 0.00</td><td>0.63 ± 0.01</td><td>0.53 ± 0.01</td><td>0.92 ± 0.00</td><td>0.84 ± 0.00</td><td>00 ± 0.00</td></tr><tr><td>TabDDPM</td><td>0.98 ± 0.03</td><td>0.67 ± 0.18</td><td>0.02 ± 0.03</td><td>0.59 ± 0.05</td><td>0.55 ± 0.02</td><td>18 ± 1.06</td></tr><tr><td>TabSyn</td><td>0.68 ± 0.06</td><td>0.61 ± 0.00</td><td>0.46 ± 0.03</td><td>0.91 ± 0.01</td><td>0.84 ± 0.01</td><td>00 ± 0.01</td></tr></tbody></table>
<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>

<figure><img src="image_21.png" /><figcaption>**Figure F.12:** Models' ranking under the light experiment setup with critical difference diagrams on C2ST, column-wise similarity, pair-wise correlation, DCR-Rate, and ML-Efficacy metrics over all datasets.</figcaption></figure>
Results per datasets and models under diverse metrics for the limited-budget search (continued).

<table><thead><tr><th rowspan="2">Dataset</th><th rowspan="2">Model</th><th colspan="6">Metrics</th></tr><tr><th>C2ST ↓</th><th>DCR-Rate ↓</th><th>ML-Efficacy ↑</th><th>Shape ↑</th><th>Pair ↑</th><th>Sampling time ↓</th></tr></thead><tbody><tr><td rowspan="4">Covertype</td><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.90 ± 0.00</td><td>1.00 ± 0.00</td><td>1.00 ± 0.01</td><td>-</td></tr><tr><td>CTGAN</td><td>0.98 ± 0.00</td><td>0.60 ± 0.00</td><td>0.69 ± 0.00</td><td>0.98 ± 0.00</td><td>0.95 ± 0.01</td><td>0.6 ± 1.58</td></tr><tr><td>TVAE</td><td>0.90 ± 0.01</td><td>0.60 ± 0.00</td><td>0.77 ± 0.01</td><td>0.98 ± 0.00</td><td>0.96 ± 0.00</td><td>0.2 ± 0.07</td></tr><tr><td>TabDDPM</td><td>0.97 ± 0.01</td><td>0.64 ± 0.02</td><td>0.69 ± 0.00</td><td>0.94 ± 0.02</td><td>0.89 ± 0.03</td><td>355 ± 10.90</td></tr><tr><td rowspan="4">Diamonds</td><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.98 ± 0.00</td><td>0.99 ± 0.00</td><td>0.77 ± 0.01</td><td>-</td></tr><tr><td>CTGAN</td><td>0.89 ± 0.01</td><td>0.64 ± 0.01</td><td>0.94 ± 0.00</td><td>0.95 ± 0.00</td><td>0.74 ± 0.02</td><td>0.0 ± 0.08</td></tr><tr><td>TVAE</td><td>0.76 ± 0.02</td><td>0.64 ± 0.00</td><td>0.96 ± 0.01</td><td>0.95 ± 0.01</td><td>0.73 ± 0.01</td><td>00 ± 0.01</td></tr><tr><td>TabDDPM</td><td>0.75 ± 0.01</td><td>0.61 ± 0.01</td><td>0.97 ± 0.00</td><td>0.97 ± 0.01</td><td>0.70 ± 0.02</td><td>10 ± 1.26</td></tr><tr><td rowspan="4">Heloc</td><td>Train Copy</td><td>0.50 ± 0.01</td><td>1.00 ± 0.00</td><td>0.70 ± 0.01</td><td>0.99 ± 0.00</td><td>0.97 ± 0.01</td><td>-</td></tr><tr><td>CTGAN</td><td>0.93 ± 0.02</td><td>0.64 ± 0.01</td><td>0.70 ± 0.01</td><td>0.97 ± 0.00</td><td>0.93 ± 0.01</td><td>00 ± 0.02</td></tr><tr><td>TVAE</td><td>0.92 ± 0.01</td><td>0.63 ± 0.01</td><td>0.69 ± 0.02</td><td>0.94 ± 0.00</td><td>0.88 ± 0.01</td><td>00 ± 0.00</td></tr><tr><td>TabDDPM</td><td>0.71 ± 0.02</td><td>0.67 ± 0.01</td><td>0.69 ± 0.02</td><td>0.95 ± 0.01</td><td>0.92 ± 0.03</td><td>03 ± 1.99</td></tr><tr><td rowspan="4">Higgs</td><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.74 ± 0.00</td><td>0.99 ± 0.00</td><td>0.99 ± 0.00</td><td>-</td></tr><tr><td>CTGAN</td><td>0.87 ± 0.00</td><td>0.60 ± 0.01</td><td>0.70 ± 0.01</td><td>0.98 ± 0.00</td><td>0.98 ± 0.00</td><td>00 ± 0.09</td></tr><tr><td>TVAE</td><td>0.92 ± 0.01</td><td>0.60 ± 0.01</td><td>0.71 ± 0.02</td><td>0.94 ± 0.01</td><td>0.97 ± 0.00</td><td>00 ± 0.03</td></tr><tr><td>TabDDPM</td><td>0.61 ± 0.02</td><td>0.62 ± 0.01</td><td>0.73 ± 0.00</td><td>0.98 ± 0.01</td><td>0.95 ± 0.01</td><td>08 ± 1.00</td></tr><tr><td rowspan="4">House 16h</td><td>Train Copy</td><td>0.50 ± 0.01</td><td>1.00 ± 0.00</td><td>0.64 ± 0.01</td><td>0.99 ± 0.01</td><td>0.99 ± 0.00</td><td>-</td></tr><tr><td>CTGAN</td><td>0.84 ± 0.02</td><td>0.62 ± 0.00</td><td>0.45 ± 0.02</td><td>0.97 ± 0.01</td><td>0.97 ± 0.01</td><td>00 ± 0.01</td></tr><tr><td>TVAE</td><td>0.84 ± 0.00</td><td>0.62 ± 0.01</td><td>0.46 ± 0.03</td><td>0.94 ± 0.00</td><td>0.98 ± 0.00</td><td>00 ± 0.00</td></tr><tr><td>TabDDPM</td><td>0.64 ± 0.01</td><td>0.61 ± 0.01</td><td>0.61 ± 0.01</td><td>0.96 ± 0.01</td><td>0.94 ± 0.03</td><td>02 ± 0.75</td></tr><tr><td rowspan="4">Insurance</td><td>Train Copy</td><td>0.50 ± 0.01</td><td>1.00 ± 0.00</td><td>0.64 ± 0.01</td><td>0.99 ± 0.01</td><td>0.99 ± 0.00</td><td>-</td></tr><tr><td>CTGAN</td><td>0.67 ± 0.02</td><td>0.92 ± 0.01</td><td>0.66 ± 0.04</td><td>0.94 ± 0.01</td><td>0.85 ± 0.02</td><td>00 ± 0.01</td></tr><tr><td>TVAE</td><td>0.65 ± 0.02</td><td>0.91 ± 0.02</td><td>0.80 ± 0.03</td><td>0.93 ± 0.01</td><td>0.88 ± 0.01</td><td>00 ± 0.00</td></tr><tr><td>TabDDPM</td><td>0.61 ± 0.02</td><td>0.62 ± 0.02</td><td>0.83 ± 0.03</td><td>0.94 ± 0.01</td><td>0.89 ± 0.02</td><td>06 ± 2.76</td></tr><tr><td rowspan="4">King</td><td>Train Copy</td><td>0.50 ± 0.01</td><td>1.00 ± 0.00</td><td>0.87 ± 0.00</td><td>0.98 ± 0.01</td><td>0.97 ± 0.01</td><td>-</td></tr><tr><td>CTGAN</td><td>0.96 ± 0.01</td><td>0.62 ± 0.00</td><td>0.66 ± 0.03</td><td>0.97 ± 0.00</td><td>0.94 ± 0.01</td><td>00 ± 0.13</td></tr><tr><td>TVAE</td><td>0.95 ± 0.01</td><td>0.61 ± 0.01</td><td>0.80 ± 0.01</td><td>0.95 ± 0.01</td><td>0.94 ± 0.00</td><td>00 ± 0.01</td></tr><tr><td>TabDDPM</td><td>1.00 ± 0.00</td><td>0.70 ± 0.46</td><td>0.03 ± 0.68</td><td>0.28 ± 0.07</td><td>0.76 ± 0.00</td><td>05 ± 0.43</td></tr><tr><td rowspan="4">Miniboo ne</td><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>0.89 ± 0.01</td><td>0.99 ± 0.00</td><td>0.99 ± 0.01</td><td>-</td></tr><tr><td>CTGAN</td><td>0.90 ± 0.01</td><td>0.60 ± 0.01</td><td>0.87 ± 0.01</td><td>0.93 ± 0.01</td><td>0.58 ± 0.01</td><td>01 ± 0.03</td></tr><tr><td>TVAE</td><td>0.94 ± 0.01</td><td>0.60 ± 0.00</td><td>0.87 ± 0.00</td><td>0.94 ± 0.00</td><td>0.59 ± 0.01</td><td>00 ± 0.03</td></tr><tr><td>TabDDPM</td><td>0.73 ± 0.01</td><td>0.62 ± 0.00</td><td>0.89 ± 0.01</td><td>0.96 ± 0.01</td><td>0.83 ± 0.05</td><td>12 ± 1.35</td></tr><tr><td></td><td>TabSyn</td><td>0.87 ± 0.01</td><td>0.60 ± 0.01</td><td>0.87 ± 0.00</td><td>0.96 ± 0.00</td><td>0.76 ± 0.14</td><td>06 ± 0.08</td></tr></tbody></table>
Results per datasets and models under diverse metrics for the limited-budget search (continued).

<table><caption>**Table F.16:** Limited-budget experiment results under various metrics. Results are averaged over 3 folds with 5 synthetic samples per fold as done in the extensive hyperparameter tuning. The best values per metric are formatted in **bold green** and the worse values are in **red**.</caption><thead><tr><th rowspan="2">Dataset</th><th rowspan="2">Model</th><th colspan="6">Metrics</th></tr><tr><th>C2ST ↓</th><th>DCR-Rate ↓</th><th>ML-Efficacy ↑</th><th>Shape ↑</th><th>Pair ↑</th><th>Sampling time ↓</th></tr></thead><tbody><tr><td rowspan="4">Moons</td><td>Train Copy</td><td>0.50 ± 0.00</td><td>1.00 ± 0.00</td><td>1.00 ± 0.00</td><td>0.99 ± 0.00</td><td>0.99 ± 0.00</td><td>-</td></tr><tr><td>CTGAN</td><td>0.70 ± 0.02</td><td>0.62 ± 0.02</td><td>1.00 ± 0.00</td><td>0.96 ± 0.01</td><td>0.96 ± 0.01</td><td>00 ± 0.02</td></tr><tr><td>TVAE</td><td>0.69 ± 0.01</td><td>0.62 ± 0.01</td><td>1.00 ± 0.00</td><td>0.96 ± 0.01</td><td>0.93 ± 0.02</td><td>00 ± 0.00</td></tr><tr><td>TabDDPM</td><td>0.53 ± 0.01</td><td>0.61 ± 0.01</td><td>1.00 ± 0.00</td><td>0.99 ± 0.00</td><td>0.98 ± 0.01</td><td>08 ± 2.13</td></tr><tr><td></td><td>TabSyn</td><td>0.59 ± 0.01</td><td>0.61 ± 0.01</td><td>1.00 ± 0.00</td><td>0.98 ± 0.01</td><td>0.97 ± 0.01</td><td>01 ± 0.00</td></tr></tbody></table>