diff --git a/ddtrace/llmobs/_llmobs.py b/ddtrace/llmobs/_llmobs.py
index d41f2bd5b6..617b12297f 100644
--- a/ddtrace/llmobs/_llmobs.py
+++ b/ddtrace/llmobs/_llmobs.py
@@ -573,13 +573,14 @@ def retrieval(
         return cls._instance._start_span("retrieval", name=name, session_id=session_id, ml_app=ml_app)
 
     @classmethod
-    def undefined_kind(
-        cls, name: Optional[str] = None, session_id: Optional[str] = None, ml_app: Optional[str] = None
+    def trace(
+        cls, kind: Optional[str] = None, name: Optional[str] = None, session_id: Optional[str] = None, ml_app: Optional[str] = None
     ) -> Span:
         """
-        Trace a generic operation. Used when the span kind is not specified, 
+        Trace any operation. Allows for span kind to be specified and otherwise defaults to empty span kind string.
 
-        :param str name: The name of the traced operation. If not provided, a default value of "undefined" will be set.
+        :param str kind: The span kind of the traced operation. If not provided, the empty string will be used.
+        :param str name: The name of the traced operation. If not provided, the empty string will be used.
         :param str session_id: The ID of the underlying user session. Required for tracking sessions.
         :param str ml_app: The name of the ML application that the agent is orchestrating. If not provided, the default
                            value will be set to the value of `DD_LLMOBS_ML_APP`.
@@ -588,7 +589,7 @@ def undefined_kind(
         """
         if cls.enabled is False:
             log.warning(SPAN_START_WHILE_DISABLED_WARNING)
-        return cls._instance._start_span("undefined", name=name, session_id=session_id, ml_app=ml_app)
+        return cls._instance._start_span(kind or "", name=name, session_id=session_id, ml_app=ml_app)
 
     @classmethod
     def annotate(
@@ -664,9 +665,6 @@ def annotate(
             span.name = _name
         if prompt is not None:
             cls._tag_prompt(span, prompt)
-        if not span_kind:
-            log.debug("Span kind not specified, skipping annotation for input/output data")
-            return
         if input_data is not None or output_data is not None:
             if span_kind == "llm":
                 cls._tag_llm_io(span, input_messages=input_data, output_messages=output_data)
diff --git a/ddtrace/llmobs/_trace_processor.py b/ddtrace/llmobs/_trace_processor.py
index 231d53d762..1ecb4126c4 100644
--- a/ddtrace/llmobs/_trace_processor.py
+++ b/ddtrace/llmobs/_trace_processor.py
@@ -76,9 +76,7 @@ def submit_llmobs_span(self, span: Span) -> None:
 
     def _llmobs_span_event(self, span: Span) -> Tuple[Dict[str, Any], bool]:
         """Span event object structure."""
-        span_kind = span._get_ctx_item(SPAN_KIND)
-        if not span_kind:
-            raise KeyError("Span kind not found in span context")
+        span_kind = span._get_ctx_item(SPAN_KIND) or ""
         meta: Dict[str, Any] = {"span.kind": span_kind, "input": {}, "output": {}}
         if span_kind in ("llm", "embedding") and span._get_ctx_item(MODEL_NAME) is not None:
             meta["model_name"] = span._get_ctx_item(MODEL_NAME)
diff --git a/ddtrace/llmobs/decorators.py b/ddtrace/llmobs/decorators.py
index c91e4635b3..8133a496c9 100644
--- a/ddtrace/llmobs/decorators.py
+++ b/ddtrace/llmobs/decorators.py
@@ -295,4 +295,4 @@ def decorator(
 tool = _llmobs_decorator("tool")
 retrieval = _llmobs_decorator("retrieval")
 agent = _llmobs_decorator("agent")
-observe = _generic_decorator("undefined_kind")
+wrap = _generic_decorator("trace")