Add diffusion-model ensembles (2D L=128, 3D L=64) and README section

DM/2D/phi4_2D_L128_kappa0.2705_lambda0.022_DM_trainL128.npy

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DM/2D/phi4_2D_L128_kappa0.2705_lambda0.022_DM_trainL8-16-32-64.npy

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DM/3D/phi4_3D_L64_kappa0.1923_lambda0.9_DM_trainL4-8-16-32.npy

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DM/3D/phi4_3D_L64_kappa0.1923_lambda0.9_DM_trainL4-8-16-32_MALAexact.npy

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DM/3D/phi4_3D_L64_kappa0.1923_lambda0.9_DM_trainL4-8-16-32_MALAscore.npy

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DM/3D/phi4_3D_L64_kappa0.1923_lambda0.9_DM_trainL64.npy

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README.md

@@ -23,6 +23,8 @@ $$S[\phi] = \sum_x \Big[-2\kappa \sum_{\mu=1}^{D} \phi_x \phi_{x+\hat\mu} + \phi
 | 3 | 0.1923 | 0.9 | 0.19225 | 16, 32, 64, 128 | 2560 | 49 GB |
 
 κ_c is the critical point estimated from Binder-cumulant crossings in the reference below.
+The folder DM/ holds the corresponding ensembles generated by the diffusion models of the
+same reference.
 
 ## Files
 
@@ -48,12 +50,15 @@ concatenated along axis 0.
 ```bash
 pip install -U huggingface_hub
 
-# everything, 51 GB
+# everything, 53 GB
 hf download phi4-generative/phi4-critical-configs --repo-type dataset --local-dir phi4-critical-configs
 
-# 2D only, 1.8 GB
+# 2D Monte Carlo ensembles only, 1.8 GB
 hf download phi4-generative/phi4-critical-configs --repo-type dataset --local-dir phi4-critical-configs --include "2D/*"
 
+# diffusion-model ensembles only, 2.4 GB
+hf download phi4-generative/phi4-critical-configs --repo-type dataset --local-dir phi4-critical-configs --include "DM/*"
+
 # a single file
 hf download phi4-generative/phi4-critical-configs --repo-type dataset --local-dir phi4-critical-configs --include "3D/*L64*"
 ```
@@ -126,6 +131,44 @@ which is the action at the top of this page without the field-independent consta
 | 64 | 0.1125(12) | 641(15) | 0.5032(48) | 0.617963(58) | −0.116385(81) |
 | 128 | 0.09725(87) | 2372(73) | 0.5658(35) | 0.617684(26) | −0.116003(38) |
 
+## Diffusion-model ensembles
+
+The folder DM/ holds the diffusion-model ensembles of the reference below at the same
+couplings, 2D at L = 128 and 3D at L = 64. Each configuration is an independent
+2000-step Euler–Maruyama integration of the reverse SDE of a score network, trained on
+Monte Carlo configurations either at the target L or only at smaller L. The two MALA
+files refine the kept configurations of the 3D ensemble trained at L ≤ 32 with 5000
+iterations of an exact Markov chain for e^{−S}, whose Metropolis-adjusted Langevin
+step uses either the learned score or −∇S as drift. The arrays are float32 with the
+same axis order as the Monte Carlo files.
+
+```
+DM/2D/phi4_2D_L128_kappa0.2705_lambda0.022_DM_trainL128.npy                 (2048, 128, 128)      134 MB
+DM/2D/phi4_2D_L128_kappa0.2705_lambda0.022_DM_trainL8-16-32-64.npy          (2048, 128, 128)      134 MB
+DM/3D/phi4_3D_L64_kappa0.1923_lambda0.9_DM_trainL64.npy                     (512, 64, 64, 64)     537 MB
+DM/3D/phi4_3D_L64_kappa0.1923_lambda0.9_DM_trainL4-8-16-32.npy              (512, 64, 64, 64)     537 MB
+DM/3D/phi4_3D_L64_kappa0.1923_lambda0.9_DM_trainL4-8-16-32_MALAscore.npy    (509, 64, 64, 64)     534 MB
+DM/3D/phi4_3D_L64_kappa0.1923_lambda0.9_DM_trainL4-8-16-32_MALAexact.npy    (509, 64, 64, 64)     534 MB
+```
+
+The file name gives the lattice sizes of the training data. The raw 3D outputs contain a
+few configurations outside the support of the Monte Carlo ensemble. As in the
+reference, the table below drops configurations with any site outside
+[−2.2576, 2.3138] or with |M| > 0.2297, the extremes of the L = 64 Monte Carlo
+ensemble of the reference. This removes 4 of 512 configurations from trainL64 and 3 of
+512 from trainL4-8-16-32. The MALA chains start from the 509 kept configurations of
+trainL4-8-16-32 and are not filtered. The observables are defined as above, and the
+Monte Carlo values at the same L are in the tables above.
+
+| ensemble | ⟨\|M\|⟩ | χ | U_L | ⟨φ_x²⟩ | ⟨S⟩/V |
+|---|---|---|---|---|---|
+| 2D trainL128 | 0.4387(46) | 762(17) | 0.4750(56) | 1.4148(12) | 0.39944(17) |
+| 2D trainL8-16-32-64 | 0.4623(41) | 673(17) | 0.5138(52) | 1.3960(14) | 0.40264(19) |
+| 3D trainL64 | 0.1229(21) | 674(38) | 0.5169(91) | 0.63820(39) | −0.09753(30) |
+| 3D trainL4-8-16-32 | 0.0942(22) | 738(36) | 0.402(16) | 0.62089(16) | −0.11130(17) |
+| 3D trainL4-8-16-32, MALA with learned score | 0.1258(21) | 680(35) | 0.5271(81) | 0.61929(11) | −0.11754(15) |
+| 3D trainL4-8-16-32, MALA with −∇S | 0.1156(18) | 643(33) | 0.509(10) | 0.617992(89) | −0.11650(13) |
+
 ## Reference
 
 The ensembles follow the setup of