diff --git a/onmt/decoders/transformer.py b/onmt/decoders/transformer.py
index 2f6187d9ed..05797d36c3 100644
--- a/onmt/decoders/transformer.py
+++ b/onmt/decoders/transformer.py
@@ -186,7 +186,8 @@ def _forward(self, *args, **kwargs):
 
     def _compute_dec_mask(self, tgt_pad_mask, future):
         tgt_len = tgt_pad_mask.size(-1)
-        if not future:  # apply future_mask, result mask in (B, T, T)
+        if not future:
+            # Add triangular future_mask and pad_mask, result mask in (B, T, T).
             future_mask = torch.ones(
                 [tgt_len, tgt_len],
                 device=tgt_pad_mask.device,
@@ -197,9 +198,14 @@ def _compute_dec_mask(self, tgt_pad_mask, future):
                 future_mask = future_mask.triu_(-self.sliding_window)
             future_mask = future_mask.bool()
             future_mask = ~future_mask.view(1, tgt_len, tgt_len)
-
+            # Patch for scaled dot product attention.
+            patch_mask = ~torch.all(
+                tgt_pad_mask + future_mask, dim=2, keepdim=True
+            ).expand_as(tgt_pad_mask + future_mask)
             dec_mask = torch.gt(tgt_pad_mask + future_mask, 0)
-        else:  # only mask padding, result mask in (B, 1, T)
+            dec_mask = torch.logical_and(dec_mask, patch_mask)
+        else:
+            # Only mask padding, result mask in (B, 1, T).
             dec_mask = tgt_pad_mask
         return dec_mask
 
@@ -717,7 +723,9 @@ def _forward(
         dec_mask = None
 
         if layer_in.size(1) > 1:
-            # masking is necessary when sequence length is greater than one
+            # Masking is necessary when sequence length is greater than one
+            # The decoding has not started yet,
+            # we compute the scores on the source tokens in one shot.
             dec_mask = self._compute_dec_mask(tgt_pad_mask, future)
             dec_mask = dec_mask.unsqueeze(1)
             dec_mask = dec_mask.expand(-1, -1, dec_mask.size(3), -1)
@@ -859,8 +867,11 @@ def detach_state(self):
     def forward(self, tgt, enc_out=None, step=None, **kwargs):
         """Decode, possibly stepwise."""
         if step == 0:
+            # decoding mode.
+            # Initialize KV cache.
             self._init_cache(tgt)
         elif step is None:
+            # training mode.
             for layer in self.transformer_layers:
                 layer.self_attn.layer_cache = (
                     False,
diff --git a/onmt/inputters/dynamic_iterator.py b/onmt/inputters/dynamic_iterator.py
index 23a9a5880b..8289d1a3ce 100644
--- a/onmt/inputters/dynamic_iterator.py
+++ b/onmt/inputters/dynamic_iterator.py
@@ -1,7 +1,7 @@
 """Module that contain iterator used for dynamic data."""
 import torch
 from itertools import cycle
-from onmt.constants import CorpusTask
+from onmt.constants import CorpusTask, ModelTask
 from onmt.inputters.text_corpus import get_corpora, build_corpora_iters
 from onmt.inputters.text_utils import (
     text_sort_key,
@@ -164,6 +164,10 @@ def __init__(
         self.skip_empty_level = skip_empty_level
         self.random_shuffler = RandomShuffler()
         self.bucket_idx = 0
+        if task != CorpusTask.TRAIN and vocabs["data_task"] == ModelTask.LANGUAGE_MODEL:
+            self.left_pad = True
+        else:
+            self.left_pad = False
 
     @classmethod
     def from_opt(
@@ -354,7 +358,9 @@ def __iter__(self):
                 # within the batch
                 if self.task == CorpusTask.TRAIN:
                     minibatch.sort(key=lambda x: self.sort_key(x[0]), reverse=True)
-                tensor_batch = tensorify(self.vocabs, minibatch, self.device)
+                tensor_batch = tensorify(
+                    self.vocabs, minibatch, self.device, self.left_pad
+                )
                 yield (tensor_batch, bucket_idx)
 
 
diff --git a/onmt/inputters/text_utils.py b/onmt/inputters/text_utils.py
index 4a145842e3..c6e9e8ff1b 100644
--- a/onmt/inputters/text_utils.py
+++ b/onmt/inputters/text_utils.py
@@ -168,7 +168,7 @@ def parse_align_idx(align_pharaoh):
     return flatten_align_idx
 
 
-def tensorify(vocabs, minibatch, device):
+def tensorify(vocabs, minibatch, device, left_pad=False):
     """
     This function transforms a batch of example in tensors
     Each example looks like
@@ -193,21 +193,37 @@ def tensorify(vocabs, minibatch, device):
         }
     """
     tensor_batch = {}
-    tbatchsrc = [
-        torch.tensor(ex["src"]["src_ids"], dtype=torch.long, device=device)
-        for ex, indice in minibatch
-    ]
+    if left_pad:
+        tbatchsrc = [
+            torch.tensor(ex["src"]["src_ids"], dtype=torch.long, device=device).flip(
+                dims=[0]
+            )
+            for ex, indice in minibatch
+        ]
+    else:
+        tbatchsrc = [
+            torch.tensor(ex["src"]["src_ids"], dtype=torch.long, device=device)
+            for ex, indice in minibatch
+        ]
     padidx = vocabs["src"][DefaultTokens.PAD]
     tbatchsrc = pad_sequence(tbatchsrc, batch_first=True, padding_value=padidx)
     if "feats" in minibatch[0][0]["src"]:
         tbatchfs = [tbatchsrc]
         for feat_id in range(len(minibatch[0][0]["src"]["feats"])):
-            tbatchfeat = [
-                torch.tensor(
-                    ex["src"]["feats"][feat_id], dtype=torch.long, device=device
-                )
-                for ex, indice in minibatch
-            ]
+            if left_pad:
+                tbatchfeat = [
+                    torch.tensor(
+                        ex["src"]["feats"][feat_id], dtype=torch.long, device=device
+                    ).flip(dims=[0])
+                    for ex, indice in minibatch
+                ]
+            else:
+                tbatchfeat = [
+                    torch.tensor(
+                        ex["src"]["feats"][feat_id], dtype=torch.long, device=device
+                    )
+                    for ex, indice in minibatch
+                ]
             padidx = vocabs["src_feats"][feat_id][DefaultTokens.PAD]
             tbatchfeat = pad_sequence(
                 tbatchfeat, batch_first=True, padding_value=padidx
@@ -218,7 +234,10 @@ def tensorify(vocabs, minibatch, device):
         # Need to add features in last dimensions
         tbatchsrc = tbatchsrc[:, :, None]
 
-    tensor_batch["src"] = tbatchsrc
+    if left_pad:
+        tensor_batch["src"] = tbatchsrc.flip(dims=[1])
+    else:
+        tensor_batch["src"] = tbatchsrc
 
     tensor_batch["srclen"] = torch.tensor(
         [len(ex["src"]["src_ids"]) for ex, indice in minibatch],
diff --git a/onmt/modules/multi_headed_attn.py b/onmt/modules/multi_headed_attn.py
index 46e1780d36..43eb7e8536 100644
--- a/onmt/modules/multi_headed_attn.py
+++ b/onmt/modules/multi_headed_attn.py
@@ -405,6 +405,7 @@ def forward(
         # 1) Project key, value, and query.
         # as a reminder at training layer_cache[0] remains False
         if self.layer_cache[0]:
+            # Retrieve keys and values from the KV cache (decoding mode only).
             if self.attn_type == "self":
                 query, key, value = (
                     self.linear_query(query),
@@ -451,6 +452,7 @@ def forward(
                 self.layer_cache[1]["keys"] = key
                 self.layer_cache[1]["values"] = value
         else:
+            # Retrieve keys and values from linear layers (training mode).
             key = self.maybe_ckpt(self.linear_keys, key)
             value = self.maybe_ckpt(self.linear_values, value)
             query = self.maybe_ckpt(self.linear_query, query)
@@ -491,12 +493,12 @@ def forward(
             self.flash2
             and l > 256  # https://github.com/Dao-AILab/flash-attention/issues/591
         )
-
         if (
             self.max_relative_positions in [-1, 0]
             and not return_attn
             and query.device != torch.device("cpu")
         ):
+            # Apply flash2 attention.
             causal = self.is_decoder and self.attn_type == "self" and mask is not None
             if self.is_decoder and self.attn_type == "self" and flash2:
                 if causal:
@@ -514,6 +516,7 @@ def forward(
                     window_size=window_size,
                 ).transpose(1, 2)
             else:
+                # Apply scaled dot product attention.
                 with torch.backends.cuda.sdp_kernel(
                     enable_flash=False, enable_math=True, enable_mem_efficient=True
                 ):
diff --git a/onmt/translate/translator.py b/onmt/translate/translator.py
index 10f89665b5..856f786b3c 100644
--- a/onmt/translate/translator.py
+++ b/onmt/translate/translator.py
@@ -658,7 +658,6 @@ def _decode_and_generate(
             step=step,
             return_attn=self.global_scorer.has_cov_pen or return_attn,
         )
-
         # Generator forward.
         if not self.copy_attn:
             if "std" in dec_attn:
@@ -988,16 +987,6 @@ def _align_forward(self, batch, predictions):
 
     def translate_batch(self, batch, attn_debug):
         """Translate a batch of sentences."""
-        batch_size = len(batch["srclen"])
-        if batch_size != 1:
-            warning_msg = (
-                "GeneratorLM does not support batch_size != 1"
-                " nicely. You can remove this limitation here."
-                " With batch_size > 1 the end of each input is"
-                " repeated until the input is finished. Then"
-                " generation will start."
-            )
-            self._log(warning_msg)
         with torch.no_grad():
             if self.sample_from_topk != 0 or self.sample_from_topp != 0:
                 decode_strategy = GreedySearchLM(
@@ -1061,7 +1050,7 @@ def tile_to_beam_size_after_initial_step(self, fn_map_state, log_probs):
             log_probs = log_probs[:, -1, :]
         return log_probs
 
-    def _translate_batch_with_strategy(self, batch, decode_strategy):
+    def _translate_batch_with_strategy(self, batch, decode_strategy, left_pad=True):
         """Translate a batch of sentences step by step using cache.
 
         Args:
@@ -1081,7 +1070,12 @@ def _translate_batch_with_strategy(self, batch, decode_strategy):
         src = batch["src"]
         src_len = batch["srclen"]
 
-        src, src_len, target_prefix = self.split_src_to_prevent_padding(src, src_len)
+        if left_pad:
+            target_prefix = None
+        else:
+            src, src_len, target_prefix = self.split_src_to_prevent_padding(
+                src, src_len
+            )
 
         # (2) init decoder
         self.model.decoder.init_state(src, None, None)
@@ -1109,7 +1103,6 @@ def _translate_batch_with_strategy(self, batch, decode_strategy):
             decoder_input = (
                 src if step == 0 else decode_strategy.current_predictions.view(-1, 1, 1)
             )
-
             log_probs, attn = self._decode_and_generate(
                 decoder_input,
                 None,