# Density Estimation on MNIST (NLL nats)

Source: [Density Estimation on MNIST (NLL nats)](<https://www.sota2.com/research/sota/density-estimation-on-mnist-nll-nats>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-02-26T05:53:17.769Z

Evaluation of Density Estimation performance on the MNIST dataset, measured using Negative Log-Likelihood in nats.

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

| Scope | Recorded value |
| --- | --- |
| Task | Density Estimation |
| Dataset (including any stated split) | MNIST |
| Metric | NLL (nats) |
| Unit | SCALAR |
| Direction | Lower is better |
| Results loaded | 5 of 5 |
| Coverage | All results currently returned for this benchmark |

Evaluation settings may differ between results. The original papers and recorded configurations are needed to establish comparability. A shared metric name alone does not establish an identical protocol.

## Metrics

- [NLL (nats)](<https://www.sota2.com/research/sota/density-estimation-on-mnist-nll-nats.md?metric=NLL%20(nats)>): Lower is better; unit: SCALAR.

## Recorded results

| Method | NLL (nats) | Result date | Report paper |
| --- | --- | --- | --- |
| CR-NVAE | 76.93 | Not recorded | 68fa6c6a1e209131cea33fb1 |
| Locally Masked PixelCNN | 77.58 | Not recorded | 68fa6c6a1e209131cea33fb1 |
| PixelVAE++ | 78 | Not recorded | 68fa6c6a1e209131cea33fb1 |
| NVAE | 78.01 | Not recorded | 68fa6c6a1e209131cea33fb1 |
| Efficient-VDVAE | 79.09 | Not recorded | 68fa6c6a1e209131cea33fb1 |

### CR-NVAE

NLL (nats): 76.93. Result ID: 698f13533a6c314849f583e9.

[Reporting paper](<https://www.sota2.com/research/paper/68fa6c6a1e209131cea33fb1.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa6cb31e209131cea35587.md>)

[Implementation](<https://github.com/sinhasam/CRVAE>)

Recorded evaluation configuration: {"data augmentation":true}. This record does not assert independent reproduction.

### Locally Masked PixelCNN

NLL (nats): 77.58. Result ID: 698f13533a6c314849f583e7.

[Reporting paper](<https://www.sota2.com/research/paper/68fa6c6a1e209131cea33fb1.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa67d41e209131cea18bde.md>)

[Implementation](<https://ajayjain.github.io/lmconv>)

Recorded evaluation configuration: {"data augmentation":false}. This record does not assert independent reproduction.

### PixelVAE++

NLL (nats): 78. Result ID: 698f13533a6c314849f583e6.

[Reporting paper](<https://www.sota2.com/research/paper/68fa6c6a1e209131cea33fb1.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa66441e209131cea0f583.md>)

Recorded evaluation configuration: {"data augmentation":false}. This record does not assert independent reproduction.

### NVAE

NLL (nats): 78.01. Result ID: 698f13533a6c314849f583e8.

[Reporting paper](<https://www.sota2.com/research/paper/68fa6c6a1e209131cea33fb1.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa690b1e209131cea1faf3.md>)

[Implementation](<https://github.com/NVlabs/NVAE>)

Recorded evaluation configuration: {"data augmentation":false}. This record does not assert independent reproduction.

### Efficient-VDVAE

NLL (nats): 79.09. Result ID: 698f13533a6c314849f583ea.

[Reporting paper](<https://www.sota2.com/research/paper/68fa6c6a1e209131cea33fb1.md>)

[Method origin paper](<https://www.sota2.com/research/paper/68fa6c6a1e209131cea33fb1.md>)

[Implementation](<https://github.com/Rayhane-mamah/Efficient-VDVAE>)

Recorded evaluation configuration: {"configuration":"section 6"}. This record does not assert independent reproduction.

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